The generator matrix

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

generates a code of length 29 over Z2[X]/(X^3) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+56x^20+90x^21+206x^22+362x^23+495x^24+864x^25+1205x^26+1646x^27+2126x^28+2186x^29+2132x^30+1778x^31+1250x^32+870x^33+482x^34+298x^35+152x^36+84x^37+70x^38+12x^39+13x^40+2x^41+1x^42+2x^44+1x^48

The gray image is a linear code over GF(2) with n=116, k=14 and d=40.
This code was found by Heurico 1.16 in 5.63 seconds.