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 X^3  1  1  1  1 X^3+X^2  1  1 X^3+X^2 X^2+X X^2  1  1  1  1  0 X^3+X  1  1 X^2 X^2+X  1 X^2+X X^3+X^2+X X^3+X^2+X  1 X^2  1  1  1  1  0  X X^2+X  1 X^2 X^3+X^2 X^2  1  X  0 X^2+X  X  X  1  1 X^2  1  1  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  1 X^3+X^2+1 X^3+1  0 X^2+X  0 X^3+X X+1 X^2+X X^3+X^2 X^2  1 X^3 X^3+X^2+X X^2+X+1  1 X^3+X X^3+X^2  1  1  1 X^2+X+1  X X^3+X  1 X^3+X^2+X X^2 X+1  X X^2+X+1 X^3+1  1  0  1 X^3+X^2+1 X^2+X X^3+X  1 X^2+X  1  1 X^3  1  1 X^3+X^2 X^3+X^2+X  0 X^3+X+1 X^3+X+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+1 X^3+X^2 X^3+1 X^2+1 X^3+X^2+X  1 X^3+X X^3 X^2  1  1 X^2+1 X^2+X  X X^2 X^3+X^2+X+1  1 X^3+X  X  1  0 X^3+X^2+X+1  0 X^3+X^2+X  X X^2  1 X^3+X X^2+X+1 X^2+1 X^2+X X^2  1 X^2+1 X^3+X+1  1  1 X^3+X^2+X X+1  X X^2+X+1  1 X+1 X^3+X^2 X^2+1 X^3+X^2  1 X+1  X  0
 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^2  X  1 X^3+1 X^2+X X+1 X+1 X^3+X^2+X  1  X X^3+X^2 X^3+X X^3+1 X^3+X^2 X+1 X+1 X^3+X^2+1 X+1 X^3+X^2+1 X^3+X X^3+X^2  X  1  1 X^3+X^2+X+1 X^3+X^2+X+1 X^3+X^2+X X^2+X X^3+1 X^3+X^2+1 X^3+X^2+X X^3+X^2+X+1 X+1 X^3+X^2+X X+1 X^3 X^2+X+1  1 X^2  0  1  0 X^2 X^2+X+1  X X^3+1 X^3+1 X^2+1 X^3+1  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+128x^86+960x^87+2072x^88+3520x^89+4452x^90+5422x^91+6027x^92+7006x^93+6995x^94+7284x^95+5974x^96+5434x^97+3971x^98+2614x^99+1554x^100+1014x^101+451x^102+344x^103+187x^104+62x^105+37x^106+17x^108+4x^109+6x^110

The gray image is a linear code over GF(2) with n=752, k=16 and d=344.
This code was found by Heurico 1.16 in 57.5 seconds.