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

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+292x^87+674x^88+884x^89+1393x^90+1492x^91+1948x^92+1846x^93+2391x^94+2152x^95+2473x^96+2278x^97+2465x^98+2016x^99+2252x^100+1812x^101+1763x^102+1364x^103+1108x^104+758x^105+574x^106+322x^107+256x^108+92x^109+78x^110+38x^111+20x^112+8x^113+8x^114+2x^115+4x^116+2x^117+2x^119

The gray image is a linear code over GF(2) with n=388, k=15 and d=174.
This code was found by Heurico 1.16 in 87.2 seconds.