The generator matrix

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

generates a code of length 31 over Z2[X]/(X^3) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+67x^26+24x^27+156x^28+64x^29+186x^30+80x^31+168x^32+64x^33+102x^34+24x^35+51x^36+26x^38+7x^40+3x^42+1x^44

The gray image is a linear code over GF(2) with n=124, k=10 and d=52.
This code was found by Heurico 1.16 in 0.0412 seconds.