The generator matrix

 1  0  1  1  1 X^2+X  1  1  0  1  1 X^2+X  1  0  1  1  1 X^2+X  1  1  1  1 X^2+X  1  X  1  1  0  1
 0  1 X+1 X^2+X  1  1  0 X+1  1 X^2+X X^2+1  1  0  1 X+1 X^2+X X^2+1  1  0 X^2+X X^2  0  1 X+1  1 X^2+1 X^2+1  1  0
 0  0 X^2  0  0  0  0  0  0 X^2 X^2  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0
 0  0  0 X^2  0  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2 X^2  0 X^2  0  0
 0  0  0  0 X^2  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2
 0  0  0  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2 X^2
 0  0  0  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0  0  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+100x^24+48x^25+224x^26+192x^27+337x^28+288x^29+288x^30+192x^31+245x^32+48x^33+64x^34+12x^36+6x^40+3x^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 0.0859 seconds.