The generator matrix
1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 X 1 1 1 1 1 0 1 1 0 1 1 1 X 1 1 1 0 1 1 1 1 0 1 1 2X 1 1 X 1 1 1 1 1 1 X 1 1 X 1 1 2X 1 1 1 1 1 1 1 1 X 0 1 X X 0 X 1 1 1 1 1 0
0 1 1 2 0 1 2 1 0 2X+1 2 1 0 2 2X+1 1 1 2X+1 2 X 2 0 1 2X+1 0 1 2X+1 2 2X+1 1 2 X+2 0 1 2X+1 2X X+2 2X+1 1 0 X+2 1 2X+2 X+1 1 2X+2 2 2X X X+1 X+2 1 X 2X+1 1 2 X 1 X X+1 X+2 X+1 X X+2 X+2 2X 1 1 2X 0 1 1 1 2 2X+1 X+1 X+1 X+2 1
0 0 2X 0 0 0 0 0 0 2X X 0 X X 2X X X X X 2X 0 X 0 X X 0 0 0 0 2X X X 0 2X 0 X X 2X X 2X X X 0 0 X 0 X 0 2X 0 0 2X X 0 X X X X X 0 0 X X 2X 2X X X X 0 2X 0 0 0 2X X X X 0 0
0 0 0 X 0 0 0 0 0 0 0 0 0 0 2X 2X 2X X X 0 X X 2X 0 X 2X 0 2X 2X 2X 0 0 X 2X X 2X 2X 0 X 0 X X X 0 X 2X 0 2X X X 2X 2X 2X 2X 2X X X 0 2X 0 2X 2X 0 0 0 2X 2X 2X 0 0 2X X 2X 0 0 0 X 0 X
0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X 0 2X X 2X 2X 2X 2X 2X X X X X 0 2X X 2X X X 2X X 2X X X X X X 2X 0 2X 2X 0 2X 0 0 X X 0 2X X X X 2X 2X X 0 X X 2X X X 0 X X 0 0 0 X X X
0 0 0 0 0 2X 0 0 0 0 0 2X 0 X 0 0 2X X 2X 0 2X 0 2X 2X 0 X 2X 2X 2X X 2X 0 X 0 X 0 0 0 2X 2X 0 X 2X 2X X X 2X 0 0 2X 2X X X X 0 X 0 2X 2X 2X 2X 2X 0 2X 2X 2X 2X X X 2X 2X 2X X 0 2X X 2X 0 0
0 0 0 0 0 0 X 0 2X 2X X 0 0 2X 2X 2X 2X 0 2X X X 2X X X 0 2X X 2X 0 2X X 0 X 2X 2X 0 2X 0 0 0 2X 0 0 X 2X 0 2X 0 X 0 X 2X 2X 0 X 0 X X 0 X 2X 0 2X 2X 2X 2X X 0 0 X X 2X 2X 0 2X 2X 0 X X
0 0 0 0 0 0 0 X X 2X 0 X 2X X X X 0 X X 0 2X X 0 2X X 2X X X 2X 0 X X X 2X 2X 0 0 X 0 X 2X 2X 0 2X 0 X 2X 0 X 0 X 0 2X 2X X X 0 X X X 0 2X X 0 2X 2X X 0 X 2X 0 X 0 0 2X 0 X 2X 0
generates a code of length 79 over Z3[X]/(X^2) who´s minimum homogenous weight is 135.
Homogenous weight enumerator: w(x)=1x^0+126x^135+324x^138+774x^141+1572x^144+3068x^147+4676x^150+7154x^153+9256x^156+10094x^159+9414x^162+6488x^165+3332x^168+1576x^171+560x^174+260x^177+176x^180+114x^183+32x^186+42x^189+8x^192+2x^195
The gray image is a linear code over GF(3) with n=237, k=10 and d=135.
This code was found by Heurico 1.16 in 73.3 seconds.