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

generates a code of length 91 over Z2[X]/(X^4) who´s minimum homogenous weight is 85.

Homogenous weight enumerator: w(x)=1x^0+80x^85+45x^86+32x^87+162x^88+112x^89+312x^90+576x^91+312x^92+112x^93+147x^94+32x^95+34x^96+80x^97+7x^102+2x^104+1x^110+1x^160

The gray image is a linear code over GF(2) with n=728, k=11 and d=340.
This code was found by Heurico 1.16 in 134 seconds.