The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2  1  X  1  1  0  1  1  1 X^2+X  1  1 X^2  0  1  1  1  X  1  1  1  X  1
 0  1  1  0  1  1  X X^2+X+1  1 X^2+X  1 X^2+X+1  0  1 X+1 X^2+1  0  1  1 X^2+X+1  1  1 X+1  0 X^2  1 X^2 X^2+X+1 X^2  1  0
 0  0  X  0  0  0  0  0  0 X^2 X^2  X  X  X  0 X^2+X X^2+X X^2  X X^2+X  X X^2+X  X X^2 X^2+X X^2 X^2  X X^2+X  0  X
 0  0  0  X  0  0  X X^2  X X^2 X^2+X  0  0  0 X^2+X X^2+X  X  X X^2+X X^2  0 X^2+X X^2 X^2+X  0  0 X^2 X^2 X^2+X  0  0
 0  0  0  0  X  0  0  X X^2 X^2  0 X^2 X^2+X  X X^2+X X^2  0  X X^2+X  X X^2 X^2  X  X  0 X^2+X X^2+X X^2+X X^2  X  X
 0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2  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+76x^24+128x^25+230x^26+360x^27+658x^28+946x^29+1082x^30+1232x^31+1117x^32+946x^33+606x^34+376x^35+246x^36+86x^37+62x^38+16x^39+14x^40+6x^41+4x^42

The gray image is a linear code over GF(2) with n=124, k=13 and d=48.
This code was found by Heurico 1.16 in 1.36 seconds.