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

generates a code of length 92 over Z2[X]/(X^4) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+182x^86+922x^87+1355x^88+1562x^89+1983x^90+1902x^91+1787x^92+1714x^93+1484x^94+1038x^95+753x^96+646x^97+406x^98+290x^99+165x^100+106x^101+56x^102+6x^103+13x^104+4x^105+6x^108+2x^111+1x^114

The gray image is a linear code over GF(2) with n=736, k=14 and d=344.
This code was found by Heurico 1.16 in 7.06 seconds.