The generator matrix

 1  0  0  0  0  1  1  1  0  1 X^2  1 X^2  1  1  0 X^2+X  1 X^2+X  X  1 X^2+X X^2+X  1  1 X^2  1  1  1  1  1  0  X  0  1 X^2  1  1  1  1  1  1  X X^2  1 X^2 X^2  1 X^2+X  1  X  1  0  1  1  X  1 X^2  X  X X^2+X X^2+X X^2+X X^2  1  X  0  1  1 X^2  1 X^2  1  1  1  1  1  1  1  1  X  1  1  X  1 X^2  1  1 X^2+X  1  1  X  1  1 X^2  1 X^2
 0  1  0  0  0  0  0 X^2 X^2  1  1  1  1  1  1  1 X^2 X+1  1  1 X^2+X  X  1 X^2+X X^2+X+1 X^2 X^2+1 X^2 X^2 X^2+X+1 X+1  1  1  1 X^2+1  1 X^2+X+1  X X^2 X+1  X X+1  1 X^2+X X^2+X+1  X X^2+X  1  1 X^2+X X^2 X^2+X X^2 X^2+X  0  1 X+1  X  1 X^2  1  0 X^2 X^2  0 X^2  X X^2+X X^2+1  1 X^2+X  1 X^2+1 X^2+X  0 X^2+X  1  1 X^2+1 X^2  1 X^2 X^2+X  1 X^2+1 X^2 X^2 X^2+X+1  1  X  X  1 X^2+1 X^2 X^2+X  1  1
 0  0  1  0  0 X^2  1 X^2+1  1  0  1 X+1 X^2+X+1 X+1 X^2 X^2  1 X+1  1  X  1 X^2+X  X X^2+X+1  0  1  0  0 X^2 X^2+X X^2+1 X^2+X X^2+X X+1 X^2  1 X^2+X  X  1 X^2+X+1 X^2 X^2+X X^2+1 X^2+X  1  1 X^2 X+1  0 X^2+1  1  0 X^2+X X^2+X X^2+1  1  0  X X+1 X^2 X^2+1  1  1  1 X^2+X  1  1 X^2+X+1 X^2+X X^2+X X^2+1 X+1 X^2+X+1 X^2+X+1  X  0 X^2+1  0  1 X^2  0 X^2+X+1  X X^2+X+1  0 X^2  1 X^2 X^2+1  1  0  X X^2+1  X X^2+X  X X+1
 0  0  0  1  0 X^2+1  1  0  1 X^2 X^2+1 X+1 X^2  0 X^2+X+1 X^2+1  1 X+1 X^2+1  1 X^2+1  1 X^2 X^2+X X^2+X  X X^2+1 X^2 X+1 X^2+1 X^2+X  X X^2+X+1  1  X X^2+X  0  1  0  0  1 X^2+1 X^2  0  X X^2+X  1 X^2+1 X+1 X+1 X^2+X+1  1  1 X^2+X  0  X X^2+X+1  1 X^2+1 X^2+X  1 X^2+X X+1 X^2+X  1 X^2+X X^2+X X^2+1 X+1 X+1 X^2+X  0  X X^2+X+1 X^2 X^2+X+1 X+1 X^2+1  1  1 X^2+1 X^2+X X^2 X^2+X+1 X^2+X  X  1 X^2+1 X^2+X X+1  0  0 X^2 X^2+X  X  X X^2+X
 0  0  0  0  1  1 X^2  1  1 X^2+1 X^2  1 X+1  X X^2 X^2+X+1  X  X X^2+X+1 X^2 X+1 X^2+X+1 X+1  0 X^2+X X^2+X+1 X^2+X+1 X+1 X^2  X X^2+X+1 X^2 X^2+X X^2+1 X^2+1  X X^2 X^2+1 X+1 X^2+1 X^2+X X^2+X+1  X  1  X X^2+1 X^2+X X+1 X+1 X^2+1 X^2+X+1 X^2+1 X^2+X X^2+X  X  1 X^2  1  0  1  X X^2+1  X X^2+X  X X+1  X X^2  X  0 X^2 X^2+1 X^2 X^2+X X^2+1 X^2+1 X+1  X  X X^2+X X^2 X+1 X^2+1 X^2+1 X^2  1  1 X^2  X X+1  0  0 X^2 X^2+X+1  1 X^2+1  X

generates a code of length 97 over Z2[X]/(X^3) who´s minimum homogenous weight is 87.

Homogenous weight enumerator: w(x)=1x^0+316x^87+582x^88+1028x^89+1108x^90+1894x^91+1662x^92+2132x^93+1858x^94+2808x^95+2058x^96+2476x^97+2087x^98+2618x^99+1838x^100+2018x^101+1432x^102+1682x^103+934x^104+894x^105+498x^106+348x^107+204x^108+134x^109+54x^110+58x^111+17x^112+18x^113+3x^114+4x^115+4x^117

The gray image is a linear code over GF(2) with n=388, k=15 and d=174.
This code was found by Heurico 1.13 in 26.9 seconds.