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.