The generator matrix

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

generates a code of length 87 over Z2[X]/(X^3) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+268x^77+487x^78+908x^79+1012x^80+1682x^81+1519x^82+2340x^83+1920x^84+2558x^85+2260x^86+2966x^87+2243x^88+2910x^89+2073x^90+2050x^91+1379x^92+1496x^93+878x^94+762x^95+376x^96+324x^97+120x^98+114x^99+41x^100+36x^101+19x^102+12x^103+4x^104+4x^105+4x^106+2x^109

The gray image is a linear code over GF(2) with n=348, k=15 and d=154.
This code was found by Heurico 1.16 in 62.9 seconds.