The generator matrix

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

generates a code of length 29 over Z2[X]/(X^3) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+106x^22+444x^23+1071x^24+1754x^25+2704x^26+3382x^27+4478x^28+4476x^29+4731x^30+3920x^31+2726x^32+1460x^33+910x^34+366x^35+136x^36+68x^37+29x^38+4x^40+2x^41

The gray image is a linear code over GF(2) with n=116, k=15 and d=44.
This code was found by Heurico 1.13 in 4.61 seconds.