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

generates a code of length 92 over Z2[X]/(X^4) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+34x^86+76x^87+54x^88+90x^89+42x^90+400x^91+692x^92+330x^93+170x^94+48x^95+15x^96+14x^97+6x^98+48x^99+4x^100+14x^101+4x^102+4x^103+1x^104+1x^168

The gray image is a linear code over GF(2) with n=736, k=11 and d=344.
This code was found by Heurico 1.16 in 1.84 seconds.