The generator matrix

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

generates a code of length 31 over Z2[X]/(X^3) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+39x^24+36x^25+59x^26+120x^27+153x^28+238x^29+277x^30+252x^31+253x^32+218x^33+142x^34+128x^35+54x^36+18x^37+26x^38+12x^39+11x^40+2x^41+7x^42+1x^44+1x^46

The gray image is a linear code over GF(2) with n=124, k=11 and d=48.
This code was found by Heurico 1.16 in 0.12 seconds.