The generator matrix

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

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+71x^24+322x^25+424x^26+566x^27+431x^28+560x^29+402x^30+562x^31+332x^32+250x^33+116x^34+34x^35+13x^36+4x^37+2x^38+6x^39

The gray image is a linear code over GF(2) with n=116, k=12 and d=48.
This code was found by Heurico 1.16 in 0.224 seconds.