The generator matrix

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

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+142x^22+520x^23+905x^24+1840x^25+2364x^26+3752x^27+4189x^28+5066x^29+4326x^30+4050x^31+2568x^32+1668x^33+680x^34+444x^35+139x^36+66x^37+40x^38+2x^39+6x^40

The gray image is a linear code over GF(2) with n=116, k=15 and d=44.
This code was found by Heurico 1.16 in 13.1 seconds.