The generator matrix

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

generates a code of length 31 over Z2[X]/(X^4) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+92x^27+334x^28+560x^29+528x^30+1000x^31+696x^32+560x^33+176x^34+92x^35+45x^36+11x^40+1x^44

The gray image is a linear code over GF(2) with n=248, k=12 and d=108.
This code was found by Heurico 1.16 in 0.125 seconds.