The generator matrix

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

generates a code of length 29 over Z2[X]/(X^3) who´s minimum homogenous weight is 23.

Homogenous weight enumerator: w(x)=1x^0+104x^23+319x^24+432x^25+630x^26+832x^27+1096x^28+1320x^29+1098x^30+952x^31+701x^32+336x^33+186x^34+96x^35+56x^36+24x^37+6x^38+3x^40

The gray image is a linear code over GF(2) with n=116, k=13 and d=46.
This code was found by Heurico 1.16 in 1.02 seconds.