The generator matrix

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

generates a code of length 29 over Z2[X]/(X^3) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+82x^24+342x^25+392x^26+502x^27+481x^28+548x^29+522x^30+450x^31+339x^32+282x^33+84x^34+38x^35+17x^36+12x^37+2x^38+2x^39

The gray image is a linear code over GF(2) with n=116, k=12 and d=48.
This code was found by Heurico 1.11 in 0.094 seconds.