The generator matrix

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

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+208x^27+247x^28+628x^29+540x^30+958x^31+559x^32+546x^33+112x^34+172x^35+68x^36+40x^37+4x^38+6x^39+4x^40+2x^41+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 35.3 seconds.