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  1  1  1  1  1  1  X  X  0  X  X  X X^2 X^2  X  X X^2  1  X  1 X^2  0  X  X  X  1  1  1 X^2  1  X  1  1  1  1  1  1  1  0 X^2  1  1  X
 0  X  0  0  0  0  0  0  0  0 X^2  X  X X^2+X  0 X^2+X X^2+X  0 X^2  X X^2+X  X  X X^2  X X^2  X  0  X X^2+X X^2  X X^2+X  0 X^2  0 X^2 X^2  0  X X^2+X X^2+X X^2+X  X  0  X  0  X  X X^2+X X^2+X X^2+X X^2+X  X X^2+X  X X^2 X^2 X^2 X^2+X  X  X  0 X^2+X X^2+X X^2  0 X^2+X X^2 X^2 X^2+X  0 X^2  X X^2  0 X^2+X X^2  0  0 X^2+X X^2+X X^2  X  X X^2  X  X
 0  0  X  0  0  0  0  0  0  0 X^2+X X^2  X  X  X  X  0  X  X  0 X^2+X X^2+X  0 X^2  X  X X^2+X X^2+X X^2 X^2+X  0  0 X^2  X  0 X^2+X  X X^2 X^2+X  X X^2  X X^2  0  X  0 X^2  0  X X^2+X  X  X  0 X^2 X^2 X^2  X  0  0 X^2+X  0 X^2  X X^2  X  X  X  0  X X^2 X^2  X X^2  X  X X^2+X X^2 X^2 X^2+X X^2 X^2 X^2+X X^2+X X^2 X^2+X X^2  0  X
 0  0  0  X  0  0  0  X X^2+X  X  X X^2+X  0  X X^2  0 X^2+X X^2+X X^2 X^2+X X^2+X X^2  0  X  0 X^2  X  X  X  X X^2  0 X^2  X X^2 X^2  X X^2  X X^2 X^2  X X^2+X  0  0  X X^2+X X^2+X X^2+X X^2  X  0  X  X X^2+X X^2+X  X  X  0 X^2 X^2 X^2 X^2 X^2+X  X  X  0  X X^2+X  0  X X^2+X  0  X  0  0 X^2  0 X^2  X X^2  X  X X^2 X^2+X  X X^2 X^2+X
 0  0  0  0  X  0  X  X  X X^2  X  X  X X^2 X^2 X^2+X X^2+X X^2 X^2+X X^2 X^2+X X^2 X^2+X  X X^2  X  0 X^2+X X^2 X^2+X X^2+X  X  X  X X^2+X  X X^2  0 X^2  X X^2 X^2  X  0  0 X^2 X^2+X X^2+X X^2 X^2  0 X^2  0  X X^2+X  0 X^2+X X^2+X  X X^2+X  0 X^2+X  X  0 X^2+X  0 X^2 X^2+X  X X^2+X X^2+X X^2+X  X X^2+X  0 X^2+X X^2  0 X^2+X X^2  X X^2+X  0 X^2+X X^2+X  0 X^2+X  X
 0  0  0  0  0  X  X X^2 X^2+X X^2+X  X  X X^2+X  0  X X^2 X^2 X^2  X X^2+X  0  0 X^2 X^2  X  0  X X^2 X^2 X^2+X X^2+X X^2+X X^2+X X^2+X X^2 X^2+X X^2 X^2  X X^2+X X^2+X  0 X^2+X  X  0 X^2+X  X X^2+X  X  0 X^2  X  X X^2  0  0 X^2  0  X X^2+X X^2+X  0  0 X^2  X  X  0  0 X^2+X  X X^2  0 X^2  0 X^2  X X^2+X X^2+X  X  0  0  X  X X^2+X  0 X^2+X X^2  0
 0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0  0 X^2  0 X^2  0  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 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+186x^76+508x^78+20x^79+692x^80+116x^81+1050x^82+400x^83+1222x^84+580x^85+1597x^86+920x^87+1957x^88+952x^89+1602x^90+592x^91+1266x^92+376x^93+850x^94+116x^95+541x^96+20x^97+394x^98+225x^100+4x^101+125x^102+49x^104+18x^106+4x^108+1x^132

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 30.9 seconds.