The generator matrix

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

generates a code of length 91 over Z2[X]/(X^4) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+188x^86+950x^87+710x^88+1344x^89+738x^90+1250x^91+645x^92+794x^93+286x^94+474x^95+212x^96+300x^97+100x^98+86x^99+51x^100+42x^101+4x^102+8x^103+5x^104+3x^106+1x^114

The gray image is a linear code over GF(2) with n=728, k=13 and d=344.
This code was found by Heurico 1.16 in 3.33 seconds.