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  1 X^2+X  1  1  1  1  1  1  X
 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 X^2+1  1 X^2+X+1  1  X X^2+X+1  1  1 X^2
 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 X^2  0 X^2+X X^2+X X^2+X X^2+X  X X^2+X X^2+X
 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 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2
 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 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2
 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 X^2  0 X^2  0 X^2  0 X^2 X^2
 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 X^2  0 X^2 X^2  0 X^2 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+68x^23+137x^24+160x^25+347x^26+512x^27+548x^28+576x^29+564x^30+504x^31+313x^32+160x^33+106x^34+64x^35+20x^36+4x^38+4x^39+5x^40+3x^42

The gray image is a linear code over GF(2) with n=116, k=12 and d=46.
This code was found by Heurico 1.16 in 0.578 seconds.