The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X X^3  1  1  1  1  1  1  X  1  0  X  1 X^2  1 X^2  1  1  1
 0  X  0 X^2+X X^2 X^3+X^2+X X^3+X^2  X  0 X^3+X X^3+X^2 X^2+X X^2+X  X X^3 X^3+X^2+X X^2  X  0 X^2+X X^3+X^2  0  X X^3+X  X X^2 X^2+X  X X^2 X^3 X^3+X
 0  0 X^3+X^2  0 X^2 X^2 X^3 X^2  0 X^3  0  0 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^2  0 X^2 X^2 X^3+X^2  0 X^3 X^3 X^2 X^3 X^3+X^2 X^3 X^3 X^3
 0  0  0 X^3  0  0 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3  0 X^3 X^3  0 X^3  0  0  0
 0  0  0  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3  0  0 X^3  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+66x^27+148x^28+280x^29+378x^30+378x^31+366x^32+216x^33+100x^34+62x^35+24x^36+16x^37+2x^38+6x^39+4x^40+1x^48

The gray image is a linear code over GF(2) with n=248, k=11 and d=108.
This code was found by Heurico 1.16 in 0.062 seconds.