The generator matrix

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

generates a code of length 87 over Z2[X]/(X^3) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+137x^78+76x^79+378x^80+260x^81+588x^82+460x^83+872x^84+456x^85+757x^86+540x^87+713x^88+560x^89+626x^90+404x^91+486x^92+184x^93+285x^94+120x^95+108x^96+12x^97+68x^98+46x^100+27x^102+15x^104+6x^106+3x^108+2x^110+1x^112+1x^124

The gray image is a linear code over GF(2) with n=348, k=13 and d=156.
This code was found by Heurico 1.16 in 6.71 seconds.