The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2  1  1  X  1  1  0 X^2+X  1  1  1  1 X^2+X  0  1  1  1  1 X^2  X  1  1 X^2+X  1  1  1  1  0  1  0  1  1  1 X^2+X  1  X  1  1  1 X^2  1  1 X^2+X  1  1  1  1  1  1  1  1  1 X^2 X^2  1 X^2+X  1  1  0  1  1  1 X^2+X  1  X  1  1 X^2+X X^2  1 X^2+X  X  1 X^2+X X^2  1  1  1  1
 0  1  1 X^2+X X^2+X+1  1  0 X+1  1  X X^2+1  1  0 X+1  1  1 X^2 X^2+X+1 X^2+X X^2+1  1  1 X^2+1 X^2+X+1 X^2+X X^2+X  1  1 X^2+1  0  1  X  1  X X^2+X+1  1 X+1  1  X X^2+X+1  0  1 X^2+1  1 X^2+X  X  1  1 X^2+1 X^2  1 X^2+1 X^2+X+1  1 X^2+X+1 X^2 X+1 X^2 X^2+X  X  1  1  0  1 X^2+X+1  X  1  1 X^2+1  X  1 X+1 X^2  0  1  1 X^2 X^2+X+1  1  1 X^2  1  X  0 X^2+X+1 X+1 X^2
 0  0  X  0 X^2+X  0 X^2+X  0 X^2+X  X X^2 X^2+X  0 X^2  0 X^2+X  X  X  X X^2 X^2  X  X X^2 X^2  0 X^2+X X^2+X  0  0  0  X X^2+X  0 X^2+X X^2  X  0  X  X X^2  0  0 X^2+X  0  X X^2+X X^2+X X^2  X  X X^2+X  0 X^2+X  X X^2 X^2 X^2+X X^2  X X^2+X  0 X^2+X X^2  0  0 X^2+X X^2 X^2  X  X X^2 X^2+X  0  0  0  X X^2 X^2 X^2  X  0 X^2+X X^2  0  0  X
 0  0  0 X^2  0  0  0  0  0  0 X^2  0 X^2  0  0  0 X^2  0 X^2 X^2  0  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2  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  0 X^2 X^2 X^2  0 X^2  0  0  0 X^2  0  0 X^2  0  0 X^2  0 X^2  0 X^2  0  0  0 X^2 X^2  0  0 X^2
 0  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0  0  0  0 X^2 X^2  0  0 X^2 X^2  0  0  0  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0  0 X^2 X^2 X^2  0  0  0 X^2  0 X^2  0  0 X^2
 0  0  0  0  0 X^2  0  0  0 X^2  0  0  0  0  0  0  0  0 X^2  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2  0 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2
 0  0  0  0  0  0 X^2  0 X^2  0  0  0  0  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0 X^2  0 X^2  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0  0 X^2  0  0 X^2 X^2  0
 0  0  0  0  0  0  0 X^2 X^2  0  0  0  0 X^2  0  0  0 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2 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  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0  0  0 X^2  0  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2  0  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+44x^77+83x^78+152x^79+289x^80+446x^81+499x^82+460x^83+528x^84+678x^85+660x^86+680x^87+701x^88+636x^89+566x^90+472x^91+413x^92+244x^93+185x^94+120x^95+101x^96+94x^97+45x^98+28x^99+6x^100+22x^101+8x^102+8x^103+3x^104+8x^105+2x^106+3x^108+4x^109+1x^112+2x^116

The gray image is a linear code over GF(2) with n=348, k=13 and d=154.
This code was found by Heurico 1.16 in 6.28 seconds.