The generator matrix

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

generates a code of length 94 over Z2[X]/(X^4) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+990x^86+1824x^87+4308x^88+5680x^89+8656x^90+10112x^91+13122x^92+13712x^93+15003x^94+13616x^95+13106x^96+10256x^97+8231x^98+5368x^99+3613x^100+1568x^101+1129x^102+304x^103+315x^104+16x^105+93x^106+8x^107+29x^108+8x^110+2x^112+2x^118

The gray image is a linear code over GF(2) with n=752, k=17 and d=344.
This code was found by Heurico 1.16 in 385 seconds.