The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  1  1  1  X  1  1  1 X^3+X^2  1  1  0  1  X  1
 0  X X^3+X^2 X^2+X  0 X^2+X X^3+X^2 X^3+X X^3+X^2 X^2+X  0 X^3+X X^3 X^3+X X^3+X^2 X^2+X  X X^3+X X^2+X  0 X^3+X  0 X^2 X^3  X X^3 X^3+X^2  X X^2 X^3+X^2 X^3+X^2+X
 0  0 X^3  0  0  0 X^3  0  0  0 X^3 X^3 X^3 X^3  0  0 X^3  0 X^3  0 X^3  0 X^3 X^3  0  0  0 X^3  0 X^3 X^3
 0  0  0 X^3  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0 X^3  0  0 X^3 X^3  0 X^3  0 X^3  0  0  0  0
 0  0  0  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3 X^3  0  0  0  0  0  0 X^3 X^3  0  0  0  0
 0  0  0  0  0 X^3 X^3  0 X^3 X^3  0  0  0  0 X^3 X^3  0 X^3 X^3 X^3 X^3  0  0 X^3  0 X^3  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 26.

Homogenous weight enumerator: w(x)=1x^0+21x^26+76x^27+77x^28+220x^29+479x^30+304x^31+488x^32+224x^33+65x^34+68x^35+7x^36+4x^37+8x^38+3x^40+1x^42+1x^46+1x^50

The gray image is a linear code over GF(2) with n=248, k=11 and d=104.
This code was found by Heurico 1.16 in 0.063 seconds.