The generator matrix

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

generates a code of length 95 over Z2[X]/(X^4) who´s minimum homogenous weight is 87.

Homogenous weight enumerator: w(x)=1x^0+116x^87+1032x^88+1952x^89+3248x^90+4444x^91+5533x^92+6484x^93+7384x^94+6736x^95+6548x^96+6216x^97+5514x^98+3916x^99+2805x^100+1644x^101+956x^102+448x^103+300x^104+140x^105+62x^106+16x^107+12x^108+8x^109+12x^110+4x^111+1x^112+4x^113

The gray image is a linear code over GF(2) with n=760, k=16 and d=348.
This code was found by Heurico 1.16 in 58.1 seconds.