The generator matrix

 1  0  1  1  1  0  1  1  0  1 X^2  1  1 X^2  1  X  1  1  0  1  1  1  X  X X^2+X  1 X^2 X^2  1
 0  1  1  0  1  1  0 X+1  1 X^2  1 X+1  0  1 X^2+X+1  1 X^2+X X^2  1 X^2+1 X^2+1 X^2+X  1 X^2+X  1  0  X  X X^2
 0  0  X  0  0  0  0  0  0 X^2 X^2  X  X X^2+X X^2 X^2+X X^2+X  X  X X^2  X X^2  X  0 X^2  X  X X^2  X
 0  0  0  X  0  0 X^2+X X^2 X^2+X  0  X  X  X  0 X^2+X X^2+X X^2 X^2 X^2+X X^2+X X^2+X  X  X  X X^2+X  X  X X^2+X  X
 0  0  0  0  X X^2+X X^2+X X^2  X  X  0 X^2  0 X^2  0  X X^2+X X^2  0  X  X  X X^2  X X^2+X  X X^2+X  0 X^2+X
 0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2 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+80x^22+124x^23+241x^24+408x^25+671x^26+936x^27+1031x^28+1226x^29+1072x^30+860x^31+694x^32+390x^33+244x^34+128x^35+49x^36+22x^37+12x^38+2x^41+1x^42

The gray image is a linear code over GF(2) with n=116, k=13 and d=44.
This code was found by Heurico 1.16 in 1.36 seconds.