The generator matrix

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

generates a code of length 89 over Z2[X]/(X^3) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+98x^78+28x^79+403x^80+224x^81+621x^82+604x^83+801x^84+1044x^85+1173x^86+1436x^87+1132x^88+1516x^89+1138x^90+1436x^91+1061x^92+1076x^93+684x^94+568x^95+485x^96+228x^97+269x^98+24x^99+158x^100+8x^101+89x^102+40x^104+20x^106+10x^108+4x^110+3x^112+1x^116+1x^124

The gray image is a linear code over GF(2) with n=356, k=14 and d=156.
This code was found by Heurico 1.16 in 22.7 seconds.