The generator matrix

 1  0  0  0  1  1  1 X^2  1  X  1 X^2  1  1  X  0  0  X X^2  1  1  1 X^2+X X^2+X  1  1  X  1 X^2  0  1
 0  1  0  0  0  1 X^2+1  1 X+1  1  0 X^2  X X^2+X+1  1  1  1  X X^2+X X^2+1 X^2+X X^2  0  1 X^2+X+1 X+1  1  X  1  0  0
 0  0  1  0  1  1 X^2 X^2+1 X^2+X X^2+X+1  0  1 X^2+1  1  0 X+1 X^2+X X^2+X  1 X^2  0  X  1 X^2+1 X+1  1  1 X^2 X^2  1  0
 0  0  0  1  1 X^2  1 X^2+X+1 X^2+X X^2+X X+1 X^2+X+1 X^2+X  1 X+1  X  X  1  X  1 X^2 X^2+X+1 X^2+1 X+1 X^2+X X^2+X+1 X^2+X X^2+1 X^2+1 X^2  0
 0  0  0  0  X  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2+X  X X^2+X X^2+X  X X^2+X  X  X X^2+X X^2 X^2+X X^2+X X^2+X  X 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+81x^24+300x^25+608x^26+1008x^27+1272x^28+1704x^29+2075x^30+2122x^31+2246x^32+1832x^33+1302x^34+940x^35+474x^36+240x^37+105x^38+42x^39+22x^40+4x^41+4x^42+2x^46

The gray image is a linear code over GF(2) with n=124, k=14 and d=48.
This code was found by Heurico 1.13 in 1.42 seconds.