The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X^2 X X 0 1 X^2 1 1 1 X^2
0 X 0 0 0 X X^2+X X X^2 X^2 0 0 X X X X^2+X 0 0 X X X X^2+X X^2 X^2+X X^2 0 X^2 X^2 X
0 0 X 0 X X X 0 X^2 0 X X^2+X X^2+X 0 X^2+X 0 X^2 X^2+X 0 X^2 0 X^2+X X^2 X^2 X X X X 0
0 0 0 X X 0 X X^2+X 0 X X X^2 X^2 X^2+X X 0 X^2 X X X^2+X X^2+X X X 0 X^2+X 0 0 X^2 X^2+X
0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 0 0 0
0 0 0 0 0 X^2 0 X^2 0 0 X^2 X^2 0 0 X^2 0 X^2 X^2 X^2 0 X^2 X^2 X^2 X^2 0 X^2 0 0 X^2
generates a code of length 29 over Z2[X]/(X^3) who´s minimum homogenous weight is 24.
Homogenous weight enumerator: w(x)=1x^0+192x^24+24x^25+198x^26+128x^27+419x^28+208x^29+334x^30+128x^31+233x^32+24x^33+98x^34+44x^36+10x^38+6x^40+1x^44
The gray image is a linear code over GF(2) with n=116, k=11 and d=48.
This code was found by Heurico 1.16 in 0.624 seconds.