The generator matrix

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

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+242x^23+546x^24+856x^25+1369x^26+1884x^27+2196x^28+2208x^29+2182x^30+1942x^31+1392x^32+832x^33+437x^34+200x^35+54x^36+24x^37+12x^38+4x^39+3x^40

The gray image is a linear code over GF(2) with n=116, k=14 and d=46.
This code was found by Heurico 1.13 in 1.59 seconds.