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

generates a code of length 94 over Z2[X]/(X^4) who´s minimum homogenous weight is 87.

Homogenous weight enumerator: w(x)=1x^0+268x^87+988x^88+1664x^89+2420x^90+2716x^91+3538x^92+3454x^93+3661x^94+3426x^95+3256x^96+2330x^97+1970x^98+1188x^99+750x^100+494x^101+315x^102+158x^103+89x^104+26x^105+21x^106+16x^107+10x^108+4x^110+4x^111+1x^114

The gray image is a linear code over GF(2) with n=752, k=15 and d=348.
This code was found by Heurico 1.16 in 21 seconds.