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.