The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  X  1  1  1  1 X^2  1  1  1  X  1  1
 0 X^2+2  0 X^2+2  0 X^2+2  2 X^2  0 X^2+2  0  0 X^2+2 X^2 X^2+2  2 X^2  2  2 X^2+2  2 X^2+2 X^2+2  2  2  0 X^2+2  2  0
 0  0  2  0  0  0  2  0  0  0  2  0  2  2  2  2  2  2  0  0  2  2  0  2  0  2  0  0  0
 0  0  0  2  0  0  0  2  0  0  2  2  2  2  0  2  0  2  2  2  0  0  2  0  0  2  0  0  0
 0  0  0  0  2  0  2  0  0  2  0  2  0  2  2  0  0  2  0  2  2  0  2  0  0  2  2  0  0
 0  0  0  0  0  2  0  2  2  2  0  2  0  2  0  2  2  0  0  2  2  0  0  0  0  2  0  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+15x^24+18x^25+33x^26+62x^27+217x^28+356x^29+207x^30+60x^31+16x^32+10x^33+12x^34+6x^35+7x^36+1x^38+2x^42+1x^50

The gray image is a code over GF(2) with n=232, k=10 and d=96.
This code was found by Heurico 1.16 in 0.016 seconds.