The generator matrix

 1  0  1  1  1  0  1  1 X^2+X  1  X  1  1  1 X^2  0  1  1  X  X  1 X^2+X  1  1  1  1 X^2  1  X
 0  1  1 X^2+X X+1  1  0 X^2+X+1  1  X  1 X^2+X+1 X^2+1 X^2  1  1 X+1  0  1  1  1  1 X^2+1  X X^2+1 X^2  1  1  0
 0  0  X  0  0 X^2+X X^2+X X^2+X X^2 X^2+X  X X^2+X  0  X  X  0 X^2  0  X  X  X X^2  0  X  0  X X^2+X X^2+X X^2
 0  0  0 X^2  0  0  0  0 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2 X^2  0  0  0 X^2 X^2
 0  0  0  0 X^2  0  0  0  0  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2
 0  0  0  0  0 X^2  0  0  0  0 X^2  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2
 0  0  0  0  0  0 X^2  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2 X^2
 0  0  0  0  0  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2  0  0 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+104x^22+16x^23+353x^24+160x^25+989x^26+496x^27+1624x^28+704x^29+1645x^30+496x^31+1005x^32+160x^33+306x^34+16x^35+80x^36+26x^38+9x^40+1x^42+1x^46

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 6.56 seconds.