The generator matrix

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

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+401x^24+308x^25+1139x^26+412x^27+1531x^28+614x^29+1589x^30+456x^31+1062x^32+218x^33+373x^34+28x^35+45x^36+10x^37+3x^38+2x^41

The gray image is a linear code over GF(2) with n=116, k=13 and d=48.
This code was found by Heurico 1.16 in 18.9 seconds.