The generator matrix

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

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+136x^24+576x^25+1205x^26+1724x^27+2717x^28+3054x^29+4517x^30+4432x^31+4936x^32+3530x^33+2647x^34+1516x^35+1007x^36+450x^37+207x^38+72x^39+35x^40+6x^41

The gray image is a linear code over GF(2) with n=124, k=15 and d=48.
This code was found by Heurico 1.16 in 14.4 seconds.