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.