The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1 X^2  1 X^2  1
 0 X^3+X^2  0  0  0 X^2 X^3+X^2 X^2  0  0  0  0 X^2 X^3+X^2 X^2 X^3+X^2  0  0 X^2 X^2  0  0 X^3+X^2 X^3+X^2 X^3 X^2 X^3 X^2 X^3 X^3+X^2 X^3 X^3+X^2 X^3 X^3+X^2 X^2 X^3+X^2 X^3  0 X^3+X^2 X^2 X^3  0 X^3+X^2 X^3+X^2  0 X^2 X^3 X^2  0 X^3 X^2 X^2 X^3+X^2 X^3+X^2 X^3  0 X^3+X^2 X^2 X^2 X^2 X^3  0 X^3+X^2 X^3 X^3+X^2 X^2  0  0 X^3 X^3  0 X^2 X^3  0 X^3 X^2 X^3+X^2 X^2 X^3 X^3 X^2  0  0 X^3 X^3 X^3 X^2 X^3 X^2 X^3+X^2 X^3
 0  0 X^3+X^2  0 X^2 X^2 X^3+X^2  0 X^2  0  0 X^3+X^2 X^2 X^3+X^2  0  0  0 X^2 X^2  0  0 X^3+X^2 X^2 X^3 X^3 X^3+X^2 X^2  0 X^3 X^2 X^2  0 X^3+X^2 X^2 X^3 X^3 X^3+X^2 X^3+X^2 X^2 X^3  0 X^3  0 X^3 X^3+X^2 X^3+X^2  0 X^3+X^2 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^3  0  0 X^3  0 X^2 X^2 X^3 X^2 X^3+X^2 X^3  0 X^2 X^2 X^3 X^2 X^2 X^3+X^2 X^2  0 X^3 X^3  0 X^2 X^3  0 X^3+X^2 X^3+X^2 X^3 X^2  0 X^3+X^2 X^3 X^2 X^2 X^3 X^3 X^3 X^3
 0  0  0 X^3+X^2 X^2  0 X^3+X^2 X^2 X^2  0 X^3+X^2  0  0 X^3+X^2 X^2  0 X^3 X^3+X^2 X^3 X^3+X^2 X^2 X^3 X^2 X^3 X^3 X^2 X^3 X^3 X^2 X^3  0 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2  0 X^3 X^3+X^2  0 X^3 X^3+X^2  0 X^2  0 X^3+X^2 X^3+X^2 X^3  0 X^2 X^3  0 X^3+X^2 X^3+X^2 X^3  0 X^3+X^2 X^3 X^2 X^3  0 X^2 X^3 X^3+X^2 X^3+X^2  0 X^3+X^2  0 X^3 X^3+X^2  0  0 X^3 X^3+X^2 X^3 X^2 X^3+X^2  0  0 X^3+X^2 X^2 X^3+X^2 X^3 X^2 X^2 X^3+X^2  0 X^2 X^3+X^2 X^3  0  0
 0  0  0  0 X^3  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0  0  0  0  0  0 X^3 X^3 X^3  0  0 X^3 X^3  0  0  0  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0  0 X^3 X^3  0  0 X^3  0 X^3 X^3  0  0  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0  0  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+114x^86+68x^88+160x^89+398x^90+704x^91+282x^92+160x^93+68x^94+25x^96+40x^98+6x^100+18x^102+1x^104+2x^106+1x^168

The gray image is a linear code over GF(2) with n=728, k=11 and d=344.
This code was found by Heurico 1.16 in 2.44 seconds.