The generator matrix

 1  0  0  1  1  1 X^3  0 X^3 X^2  1  1  1  1  1  X X^3+X^2+X  1  1 X^2+X  1  1  1 X^3+X^2+X  1  X  1 X^2+X X^2 X^3 X^2  1  X  1  1  1 X^2+X X^2+X  1  1  1 X^2+X  1  1  1  0 X^3+X^2+X  1 X^2  1  1  1  1 X^2  1  0  1  1 X^3+X X^3  1  X  1  1  0  1 X^3 X^3 X^2  1 X^3+X  1  X  X X^3+X^2+X X^3+X^2  1  1 X^2  1 X^3+X^2 X^2+X  1  1  1  1 X^3+X^2  1  1 X^3+X^2+X  1  1  1
 0  1  0  0 X^3+X^2+1 X^2+1  1 X^3+X^2+X  1  1 X^3 X^2+1 X^2+1  0 X^2+X+1  1 X^3 X^3+X+1 X^3+X^2+X  1 X^3+X X^3+X+1 X^3+X^2+X  1  X X^3+X^2+X X^3+X^2+X+1  1  1 X^3+X^2  1 X^3+X X^2  1  X X^3+1  1 X^3+X X^3+X^2+X+1 X^3+X  0  1 X^2+X+1 X^3 X^3+X^2 X^2+X  1 X+1  1  1  1  0  X  1 X^3+X  1 X^3+X^2+1 X+1  1  1 X^3+X^2+X  1 X^2+X+1 X+1  1  X  X  1  1 X^3+X^2+1  X X^2+1  1 X^3+X^2+X  1 X^3+X^2 X^2 X^3+X X^2 X^3+1  0  1 X^3 X+1 X+1  0  1  1 X^3+X^2  1 X^3+X^2+1 X+1 X^3
 0  0  1 X+1 X^3+X+1 X^3 X^2+X+1  1 X^2+X  1 X^3+X^2+X X^2+X X^3+X^2+1 X^3+1 X^2+X+1  X  1 X^2 X+1 X^3+X+1  X X^3+X^2+X  1 X^3 X^3+X^2  1 X^3+1  1  X  1 X^2+1 X^2+1  1 X^2 X^3 X^2+1 X^2+X+1  1 X^3+X^2+X X^3+X X^3+X^2 X^3+X^2+X X^3+X^2+X+1 X^3+X^2+X+1  X  1  1 X^3+X^2  0 X^3+X+1  0 X^3+1 X^3+X^2+X X^3+X^2+X X^2+1 X^3+X^2+X+1 X^2+X X^3+X^2+1 X^2 X+1 X^3+X+1 X^2+1 X^3+X+1 X^3+X^2+1 X^2+1 X^3+X+1  1 X+1 X^2 X+1  1 X^3+X^2+1 X^2+1  1 X^3+X^2  1 X^2+1 X^3+X+1  1  1  1 X^3+X^2+X X^2+X+1 X^3+X X^3+X+1 X^3+1 X^3+X+1  0 X^3+X+1 X^2 X^3+X X^2 X^3
 0  0  0 X^2 X^2  0 X^2 X^3+X^2 X^3+X^2  0 X^2 X^2 X^3 X^3 X^3 X^2  0 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2  0 X^3  0 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^3 X^3 X^3 X^3+X^2 X^3 X^3+X^2  0  0  0  0  0 X^3+X^2  0 X^2 X^3  0 X^2 X^2 X^2 X^3+X^2  0 X^2 X^2 X^2 X^3 X^2 X^3 X^3+X^2  0 X^3+X^2  0 X^3  0 X^3+X^2 X^3 X^3+X^2 X^3  0 X^3+X^2 X^2 X^3+X^2 X^2 X^3+X^2 X^3 X^3 X^2  0 X^3+X^2 X^2 X^2 X^3 X^3+X^2 X^3  0 X^3+X^2  0  0 X^3  0 X^2 X^3  0 X^3+X^2 X^3

generates a code of length 93 over Z2[X]/(X^4) who´s minimum homogenous weight is 87.

Homogenous weight enumerator: w(x)=1x^0+188x^87+917x^88+1252x^89+1637x^90+1942x^91+2246x^92+1796x^93+1403x^94+1336x^95+1128x^96+850x^97+624x^98+378x^99+317x^100+148x^101+136x^102+28x^103+22x^104+18x^105+12x^106+1x^108+3x^110+1x^114

The gray image is a linear code over GF(2) with n=744, k=14 and d=348.
This code was found by Heurico 1.16 in 6.99 seconds.