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

generates a code of length 87 over Z2[X]/(X^3) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+76x^74+78x^75+167x^76+268x^77+313x^78+400x^79+476x^80+610x^81+736x^82+980x^83+1027x^84+1188x^85+1283x^86+1284x^87+1381x^88+1206x^89+1079x^90+824x^91+692x^92+580x^93+411x^94+392x^95+233x^96+182x^97+157x^98+116x^99+95x^100+60x^101+33x^102+20x^103+21x^104+2x^105+6x^106+2x^107+3x^108+1x^114+1x^122

The gray image is a linear code over GF(2) with n=348, k=14 and d=148.
This code was found by Heurico 1.16 in 30.2 seconds.