The generator matrix

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

generates a code of length 29 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+44x^24+48x^25+136x^26+136x^27+472x^28+424x^29+461x^30+112x^31+115x^32+32x^33+32x^34+8x^35+8x^36+8x^37+10x^38+1x^46

The gray image is a code over GF(2) with n=232, k=11 and d=96.
This code was found by Heurico 1.16 in 0.062 seconds.