The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2  1  X  1  1 X^2  1  0  1  1  1  X X^2+X  0  1  1  1  0  X X^2 X^2+X  X  1
 0  1  1 X^2+X X^2+X+1  1  0 X+1  1 X^2+1  1  X X^2  1 X+1  1  0 X^2+X+1 X^2+X  1  1  1  1  X X^2+1  0 X^2+X X^2  1 X^2+X  0
 0  0  X  0 X^2+X  0 X^2+X  0  X X^2  X  X  X X^2+X  0  0 X^2  X X^2 X^2+X  0  X X^2+X X^2+X X^2  X X^2+X  X X^2  0  0
 0  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0 X^2  0  0 X^2  0  0 X^2  0  0  0
 0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0
 0  0  0  0  0 X^2  0 X^2  0 X^2  0  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0
 0  0  0  0  0  0 X^2  0 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0  0  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+32x^24+82x^25+186x^26+186x^27+383x^28+310x^29+725x^30+386x^31+592x^32+306x^33+460x^34+190x^35+126x^36+66x^37+34x^38+6x^39+14x^40+4x^41+2x^42+3x^44+1x^46+1x^48

The gray image is a linear code over GF(2) with n=124, k=12 and d=48.
This code was found by Heurico 1.16 in 0.305 seconds.