The generator matrix

 1  0  0  1  1  1 X^2  0 X^3 X^2  1  1 X^3+X  1  1  1  1 X^3+X^2+X  1 X^2+X  1 X^3+X^2+X  1 X^3  1 X^3 X^3+X  1  1  1  1
 0  1  0  0 X^3+X^2+1  1  1 X^2+X  1  1 X^3+X^2+1 X^3+1 X^3+X X^3 X^2 X^2 X^2+X+1  1 X^3+X^2+X+1  1 X^2+X  1 X+1  X  0  1 X^2+X X^2+X X+1 X^3+1  0
 0  0  1 X+1 X^2+X+1 X^2 X^2+X+1  1 X^3+X^2+X  1  1 X^3+X  1 X^3+X^2+X  1 X^2+X+1 X^3+X^2+X+1 X^2 X^2+X X+1  X  X X^3+X+1  1 X^2+X X^3+X  1 X^2+1 X^3+1 X^2+X+1 X^3+X^2
 0  0  0 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0  0 X^3  0  0  0  0  0 X^3  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+174x^27+534x^28+1280x^29+1310x^30+1842x^31+1199x^32+1052x^33+493x^34+214x^35+34x^36+36x^37+12x^38+10x^39+1x^42

The gray image is a linear code over GF(2) with n=248, k=13 and d=108.
This code was found by Heurico 1.16 in 0.5 seconds.