The generator matrix

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

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+48x^21+111x^22+218x^23+281x^24+428x^25+600x^26+828x^27+1065x^28+1036x^29+1030x^30+832x^31+641x^32+484x^33+277x^34+164x^35+54x^36+52x^37+27x^38+6x^39+5x^40+2x^42+1x^44+1x^50

The gray image is a linear code over GF(2) with n=116, k=13 and d=42.
This code was found by Heurico 1.16 in 2.02 seconds.