The generator matrix

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

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+50x^25+132x^26+206x^27+379x^28+502x^29+529x^30+552x^31+521x^32+492x^33+365x^34+190x^35+76x^36+38x^37+27x^38+12x^39+14x^40+6x^41+3x^42+1x^44

The gray image is a linear code over GF(2) with n=124, k=12 and d=50.
This code was found by Heurico 1.16 in 0.324 seconds.