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

generates a code of length 88 over Z2[X]/(X^3) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+60x^78+32x^79+287x^80+236x^81+405x^82+416x^83+492x^84+588x^85+610x^86+780x^87+600x^88+772x^89+535x^90+588x^91+413x^92+420x^93+295x^94+228x^95+184x^96+32x^97+99x^98+4x^99+52x^100+32x^102+14x^104+9x^106+1x^108+3x^110+2x^112+2x^116

The gray image is a linear code over GF(2) with n=352, k=13 and d=156.
This code was found by Heurico 1.16 in 6.23 seconds.