The generator matrix

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

generates a code of length 87 over Z2[X]/(X^3) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+36x^76+292x^77+485x^78+834x^79+1135x^80+1594x^81+1709x^82+2048x^83+2171x^84+2634x^85+2270x^86+2694x^87+2198x^88+2662x^89+2214x^90+2044x^91+1484x^92+1450x^93+923x^94+750x^95+474x^96+284x^97+184x^98+76x^99+44x^100+40x^101+18x^102+2x^103+8x^104+4x^105+4x^106+1x^114+1x^116

The gray image is a linear code over GF(2) with n=348, k=15 and d=152.
This code was found by Heurico 1.16 in 60.9 seconds.