The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1 X^2  1  1  1  X X^2  1  1  X  1  0  1  X
 0  X  0  X  0  0  X X^2+X  0 X^2  X X^2+X  0 X^2+X  X X^2  X X^2  0  0 X^2  X  0 X^2+X  X X^2  0  0 X^2+X
 0  0  X  X  0 X^2+X  X  0 X^2  X  X  0 X^2 X^2+X  X  X  X  X X^2  0  X X^2+X X^2+X  0  X  X  X X^2+X  0
 0  0  0 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2
 0  0  0  0 X^2  0  0  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2
 0  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2
 0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2 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+60x^23+76x^24+76x^25+161x^26+264x^27+281x^28+236x^29+292x^30+256x^31+135x^32+68x^33+54x^34+56x^35+14x^36+4x^37+4x^38+4x^39+4x^40+1x^42+1x^44

The gray image is a linear code over GF(2) with n=116, k=11 and d=46.
This code was found by Heurico 1.16 in 21.2 seconds.