The generator matrix

 1  0  1  1  1 X^2+X  1  1  0  1  1 X^2+X  1 X^2+X  1  1  1  0  1 X^2  1 X^2+X  1  1  X  1  1  1  0  1  1 X^2+X  1  1  1  0  1  1  0  1 X^2+X  1  1  1  0  1 X^2+X  1  1  1  0  1  1  0  1  1  1  0 X^2+X  1  X X^2  1  1  1  1  1  1 X^2+X  1  1  X X^2+X  1  1  1  1  1  X  1  1 X^2+X  1  1 X^2+X  1  0  0
 0  1 X+1 X^2+X  1  1  0 X+1  1 X^2+X X^2+1  1 X^2+X  1 X+1  0 X^2+1  1 X^2  1 X^2+1  1 X^2+X X+1  1 X+1 X^2+X X^2+X+1  1  0 X^2+1  1 X^2+X X^2+1  0  1  X  0  1 X+1  1  0 X+1 X^2+1  1 X^2+1  1 X^2 X^2+X X+1  1 X^2+X X^2+X+1  1 X^2+X X^2+1 X+1  1  1  0  1  1  0 X^2+X X^2+X+1 X^2+X+1 X^2+X  0  1  0 X^2  1  1  X  X  X X^2+X+1 X+1  1  X X^2+X+1  1 X^2+X+1 X^2+X  1  0  1  1
 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 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2  0  0  0 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2  0  0  0  0  0 X^2 X^2
 0  0  0 X^2  0  0  0  0  0  0  0  0 X^2  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0  0  0 X^2  0 X^2  0 X^2 X^2  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  0
 0  0  0  0 X^2  0  0  0  0  0  0  0  0  0  0 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  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 X^2 X^2  0  0 X^2  0 X^2  0 X^2 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2  0
 0  0  0  0  0 X^2  0  0  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2  0  0 X^2  0
 0  0  0  0  0  0 X^2  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2 X^2  0  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0  0 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 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0  0 X^2  0  0  0 X^2
 0  0  0  0  0  0  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2  0 X^2  0  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0  0  0 X^2 X^2
 0  0  0  0  0  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0  0  0  0 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2  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 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2
 0  0  0  0  0  0  0  0  0 X^2 X^2  0 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 X^2 X^2 X^2  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0  0  0 X^2  0  0 X^2  0  0  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+145x^76+4x^77+140x^78+116x^79+517x^80+372x^81+556x^82+740x^83+978x^84+1240x^85+1096x^86+1624x^87+1442x^88+1624x^89+1096x^90+1240x^91+907x^92+740x^93+556x^94+372x^95+434x^96+116x^97+140x^98+4x^99+99x^100+48x^104+25x^108+6x^112+5x^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 24 seconds.