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 1 0 1 1 1 1 1 1 1 1 1 0 2X 1 1 1 0 X 1 1 1 1
0 1 1 2 0 1 2 1 0 2X+1 2 1 0 2 2X+1 1 1 X+2 0 2X+1 2 2X+1 1 0 2 0 1 2X+1 2X+1 X+1 2 X 2X+1 2X X 2X 1 1 2 2X X+2 1 0 2X+1 0 0 0
0 0 2X 0 0 0 0 0 0 2X X 2X 2X 2X 2X 0 2X 0 X 2X X 0 2X 0 2X 2X 2X 2X 0 0 X 2X 0 X X X X 2X 0 X 0 X X X X 0 0
0 0 0 X 0 0 0 0 0 0 0 0 0 0 2X X 2X X 0 X 0 2X 2X X 2X 0 X 2X 0 X X 0 X X X 2X X 0 X X X 0 0 2X X X 0
0 0 0 0 X 0 0 0 0 0 0 0 0 0 2X 2X X 0 2X X 2X X 0 X X 2X X 0 2X 0 0 X 2X 2X X 0 X X 2X X X X 2X 0 2X 2X 0
0 0 0 0 0 2X 0 0 X 2X 2X X 2X 0 2X 2X 2X X X 0 0 2X 2X 0 2X X 2X 0 2X 2X 2X 0 0 2X 0 2X X 2X 2X X 2X X X 0 2X X 0
0 0 0 0 0 0 X 0 X 0 X X X 2X 2X 0 X 2X 2X 0 2X X 2X 0 0 2X 0 2X 2X X 0 X 0 2X 0 2X X X X 0 2X X 0 2X 2X X 0
0 0 0 0 0 0 0 X X X X 0 2X X 2X X X X 0 2X 0 X 0 0 0 0 2X 2X 2X 0 2X X 2X 0 0 2X 0 0 2X 2X 0 2X 2X X X X 0
generates a code of length 47 over Z3[X]/(X^2) who´s minimum homogenous weight is 72.
Homogenous weight enumerator: w(x)=1x^0+32x^72+18x^74+186x^75+66x^77+356x^78+48x^79+210x^80+584x^81+204x^82+498x^83+1338x^84+630x^85+1086x^86+2616x^87+1434x^88+1716x^89+5158x^90+2598x^91+2364x^92+6744x^93+2988x^94+2544x^95+7236x^96+2802x^97+2202x^98+4882x^99+1734x^100+1482x^101+2162x^102+594x^103+678x^104+816x^105+90x^106+246x^107+344x^108+12x^110+194x^111+92x^114+40x^117+14x^120+8x^123+2x^126
The gray image is a linear code over GF(3) with n=141, k=10 and d=72.
This code was found by Heurico 1.16 in 34.2 seconds.