The generator matrix
1 0 1 1 1 1 1 0 1 0 1 1 1 1 1 0 X 1 1 0 1 1 1 X 1 1 0 2X 1 1 1 1 1 X 1 1 X 1 1 1 X 1
0 1 1 2 0 1 2 1 2X+1 1 0 2 X+2 2X+1 0 1 1 0 2 1 2X+1 2 2X+1 1 2 X 1 1 2X+1 X+1 2X 2X+2 0 1 2X+2 X 1 2X+2 X+2 2X+1 1 0
0 0 2X 0 0 0 0 0 0 0 2X X X 2X 2X 2X 2X 2X 2X X 0 X 0 0 2X X 2X 2X 2X X X 2X 0 2X X 0 X X 0 0 X 0
0 0 0 X 0 0 0 X 2X X 0 2X X 2X 2X 0 2X 2X 0 2X X X 2X X 2X 0 X X X 2X 0 0 X X X 2X 0 0 X 0 0 0
0 0 0 0 X 0 X X X X X 2X 0 X X 0 2X 0 0 0 0 2X 2X 2X 2X 2X 2X 0 X 0 0 X 2X 2X X 0 0 2X 0 X 2X 0
0 0 0 0 0 2X 2X 0 2X X 0 2X X X 2X 2X X X 2X 0 2X 0 X 0 2X 0 2X 2X 0 2X X 2X X X 0 0 0 X X 2X X X
generates a code of length 42 over Z3[X]/(X^2) who´s minimum homogenous weight is 72.
Homogenous weight enumerator: w(x)=1x^0+50x^72+12x^73+54x^74+292x^75+120x^76+150x^77+470x^78+216x^79+246x^80+588x^81+264x^82+282x^83+796x^84+390x^85+378x^86+764x^87+324x^88+240x^89+420x^90+102x^91+96x^92+158x^93+30x^94+12x^95+38x^96+28x^99+28x^102+6x^105+2x^108+4x^111
The gray image is a linear code over GF(3) with n=126, k=8 and d=72.
This code was found by Heurico 1.16 in 0.451 seconds.