The generator matrix

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

generates a code of length 91 over Z2[X]/(X^4) who´s minimum homogenous weight is 83.

Homogenous weight enumerator: w(x)=1x^0+704x^83+1968x^84+3856x^85+5779x^86+8344x^87+10723x^88+12546x^89+14539x^90+15050x^91+14186x^92+13354x^93+9998x^94+7842x^95+5458x^96+3158x^97+1835x^98+958x^99+432x^100+174x^101+67x^102+40x^103+28x^104+16x^105+4x^106+4x^107+4x^108+2x^110+2x^111

The gray image is a linear code over GF(2) with n=728, k=17 and d=332.
This code was found by Heurico 1.16 in 424 seconds.