The generator matrix

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

generates a code of length 88 over Z2[X]/(X^3) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+202x^76+4x^77+488x^78+68x^79+715x^80+140x^81+962x^82+400x^83+1389x^84+636x^85+1578x^86+800x^87+1843x^88+808x^89+1620x^90+648x^91+1253x^92+380x^93+820x^94+124x^95+588x^96+76x^97+432x^98+8x^99+224x^100+4x^101+96x^102+43x^104+18x^106+10x^108+2x^110+2x^112+1x^116+1x^124

The gray image is a linear code over GF(2) with n=352, k=14 and d=152.
This code was found by Heurico 1.16 in 36.2 seconds.