The generator matrix

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

generates a code of length 93 over Z2[X]/(X^4) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+193x^86+972x^87+1651x^88+2422x^89+3063x^90+3252x^91+3453x^92+3598x^93+3746x^94+3080x^95+2338x^96+1822x^97+1303x^98+818x^99+433x^100+318x^101+138x^102+76x^103+39x^104+12x^105+19x^106+6x^107+4x^108+4x^109+1x^110+4x^111+1x^112+1x^114

The gray image is a linear code over GF(2) with n=744, k=15 and d=344.
This code was found by Heurico 1.16 in 22.6 seconds.