The generator matrix

 1  0  0  0  1  1  1 X^2  1  X  1  1  1  X X^2  1  1  1 X^2+X  1  1  1  0 X^2+X  1  0  0  1  0
 0  1  0  0  0  1  1  1 X^2+X X^2+X X+1 X^2+X  1  1  1  1 X^2+X X^2+1  1  0 X^2+X+1 X+1  1  X X^2 X^2+X  0  0  X
 0  0  1  0  1  1  0  1 X^2  1 X^2+X X+1 X^2+X+1 X^2+X+1  0  X X^2+X  1 X^2+X+1 X^2+X+1 X^2+1 X+1  0  1 X+1  X  1  X X^2
 0  0  0  1  1  0  1 X+1 X^2+X+1  1 X^2+X  0 X+1 X^2+X X^2+1 X^2 X+1  X X^2+X+1 X^2+X+1 X^2+X+1 X^2+1 X^2+X+1 X^2+X X^2+X+1  1 X^2+X+1  1 X^2
 0  0  0  0 X^2  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0
 0  0  0  0  0 X^2  0  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2
 0  0  0  0  0  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  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+215x^22+504x^23+1023x^24+1584x^25+2611x^26+3724x^27+4215x^28+4728x^29+4577x^30+3748x^31+2598x^32+1696x^33+889x^34+340x^35+219x^36+56x^37+28x^38+4x^39+6x^40+2x^44

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 12.9 seconds.