The generator matrix

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

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+67x^26+520x^27+1215x^28+2014x^29+2778x^30+3402x^31+2641x^32+2046x^33+1027x^34+408x^35+191x^36+48x^37+16x^38+6x^39+2x^41+2x^45

The gray image is a linear code over GF(2) with n=248, k=14 and d=104.
This code was found by Heurico 1.16 in 1.33 seconds.