The generator matrix

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

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+84x^23+320x^24+420x^25+659x^26+826x^27+1306x^28+1008x^29+1323x^30+738x^31+765x^32+372x^33+185x^34+110x^35+38x^36+24x^37+9x^38+2x^39+2x^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 1.15 seconds.