The generator matrix

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

generates a code of length 29 over Z2[X]/(X^3) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+50x^21+231x^22+460x^23+956x^24+1704x^25+2352x^26+3470x^27+4710x^28+4952x^29+4492x^30+3618x^31+2505x^32+1648x^33+912x^34+386x^35+210x^36+94x^37+12x^38+2x^39+2x^40+1x^54

The gray image is a linear code over GF(2) with n=116, k=15 and d=42.
This code was found by Heurico 1.16 in 14.1 seconds.