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 1 0 1 1 1 0 0 1 1 2X 1 1 1 1 1 2X 1 1 2X 1 1 1 1 0 0 1 1 1 2X 1 1 1 2X 1 0 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 0 2X+1 2 1 0 2 2X+1 1 1 X X 1 2 2X+1 X+1 2X+2 2X 1 0 X+1 1 X 2X+2 X 0 1 1 X+1 2X+1 2X 1 X 1 X 1 2 1 0 0
0 0 2X 0 0 0 0 0 0 2X X 2X 2X 2X 2X 0 2X 0 2X 2X 0 2X 2X 0 2X 0 X 0 2X 0 0 X 2X 2X X 0 X 2X 2X 0 2X 0 0 2X 0 X 2X 2X X 2X X X X 2X X X X X 0
0 0 0 X 0 0 0 0 0 0 0 0 0 0 2X X 2X X 0 X X 2X 2X X 0 X X 0 X 0 X 0 2X X X X 0 2X X 0 2X X X 2X 2X 2X X 2X 0 0 X 2X 0 0 0 X 2X 0 0
0 0 0 0 X 0 0 0 0 0 0 0 0 0 2X 2X X 0 2X X 2X 0 2X X 2X 0 2X 2X 0 2X 2X X 2X 2X X 0 2X 0 2X X X X 0 0 X 0 X 2X 2X 2X 0 2X 0 2X 0 X 2X 2X 0
0 0 0 0 0 2X 0 0 X 2X 2X X 2X 0 2X 2X 2X X 0 0 0 X X X 0 0 0 X 2X X 2X 2X 0 0 2X X 0 X X 2X X X X 2X 0 X 0 0 0 0 0 2X 0 X 2X 0 2X 0 2X
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 X 2X 0 2X X 0 2X X 2X X 2X 0 0 0 0 2X X 2X 2X 2X 0 X X 2X X X X 2X X X X 0 0
0 0 0 0 0 0 0 X X X X 0 2X X 2X X X X X 2X 2X 2X X 0 X X 2X X X 0 0 X 0 0 X 0 X 0 0 X 2X X X 0 2X X X 0 0 0 2X 2X 0 0 X 2X X X 0
generates a code of length 59 over Z3[X]/(X^2) who´s minimum homogenous weight is 96.
Homogenous weight enumerator: w(x)=1x^0+78x^96+6x^98+216x^99+102x^101+402x^102+606x^104+574x^105+1356x^107+816x^108+3036x^110+1634x^111+5034x^113+2794x^114+7422x^116+3776x^117+8514x^119+3818x^120+6996x^122+2644x^123+3942x^125+1422x^126+1788x^128+584x^129+486x^131+424x^132+72x^134+244x^135+6x^137+144x^138+70x^141+30x^144+6x^147+4x^150+2x^153
The gray image is a linear code over GF(3) with n=177, k=10 and d=96.
This code was found by Heurico 1.16 in 49.3 seconds.