The generator matrix

 1  0  1  1  1 X^3+X^2+X  1  1  0  1  1 X^3+X^2+X  1 X^3  1  0 X^2+X  1  1  1  1 X^3+X^2+X  1  1  1  1 X^2  1 X^2 X^2  1
 0  1 X+1 X^3+X^2+X X^2+1  1 X^3+X+1  0  1 X^3+1 X^3+X^2+X  1 X^3+X^2  1 X^3+X^2+1  1  1 X^3+X^2+X+1 X^2+X X^3 X^3+X^2+1  1  0 X^2+X+1 X^2+X+1 X^3+X^2+X  1 X^3+X X^2 X^2 X^2+X+1
 0  0 X^2  0  0 X^3  0 X^2 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^3+X^2 X^3  0 X^2 X^3 X^3  0 X^3+X^2 X^3+X^2 X^3+X^2 X^3 X^3+X^2  0 X^2 X^3+X^2  0 X^2 X^2 X^2
 0  0  0 X^3+X^2 X^3 X^2 X^2 X^3+X^2 X^3+X^2 X^2 X^3 X^3 X^3+X^2 X^3+X^2 X^2  0  0 X^3  0  0 X^3 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^2  0 X^3 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+110x^27+335x^28+628x^29+740x^30+614x^31+654x^32+576x^33+248x^34+98x^35+61x^36+12x^37+4x^38+10x^39+5x^40

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 0.094 seconds.