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

generates a code of length 92 over Z2[X]/(X^4) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+193x^88+96x^89+148x^90+288x^91+610x^92+288x^93+136x^94+96x^95+180x^96+4x^98+6x^100+1x^104+1x^176

The gray image is a linear code over GF(2) with n=736, k=11 and d=352.
This code was found by Heurico 1.16 in 1.78 seconds.