The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 X^2 X 1 X 1 0 X 1 1 1 1 X
0 X 0 0 0 X X^2+X X X^2 X^2 X 0 0 X X X^2+X X^2 0 X X^2 X X^2 X^2+X X^2+X X^2 X X X 0 X 0
0 0 X 0 X X X 0 X^2 0 X^2+X X X^2+X 0 X^2+X 0 X^2 X^2+X X^2 X X 0 X^2+X X^2 X^2 0 X^2+X X X X X
0 0 0 X X 0 X X^2+X 0 X X^2 X X^2 X^2+X X 0 X^2+X X X^2 X^2+X X^2 X^2+X X 0 X X^2+X 0 0 X^2+X X^2+X X
0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 X^2 0 X^2 0 X^2 0 0 0 X^2 0 0 X^2 X^2 0 X^2 X^2 0 0 X^2 0
0 0 0 0 0 X^2 0 X^2 0 0 0 X^2 X^2 0 X^2 0 X^2 X^2 X^2 0 0 X^2 X^2 X^2 0 X^2 X^2 0 0 0 X^2
generates a code of length 31 over Z2[X]/(X^3) who´s minimum homogenous weight is 25.
Homogenous weight enumerator: w(x)=1x^0+44x^25+84x^26+116x^27+169x^28+208x^29+264x^30+344x^31+277x^32+150x^33+140x^34+94x^35+59x^36+44x^37+24x^38+20x^39+5x^40+2x^41+2x^43+1x^48
The gray image is a linear code over GF(2) with n=124, k=11 and d=50.
This code was found by Heurico 1.16 in 0.123 seconds.