The generator matrix

 1  0  1  1  1 X^2+X+2  1  1  0  1  1 X^2+X+2  2  1  1  0 X^2+X  1  1  1  1 X^2+2  1  1  1  1  1  1
 0  1 X+1 X^2+X+2 X^2+1  1 X+3  0  1  3 X^2+X+2  1  1 X^2+2 X^2+3  1  1 X^2+X+3  2 X^2+X X^2+3  1  X X^2+3 X^2+X+1 X^2+X+2 X+1  0
 0  0 X^2  0  0  2  0 X^2 X^2+2 X^2+2 X^2 X^2+2  2 X^2+2  0 X^2  2  2 X^2+2  0 X^2+2 X^2  2 X^2 X^2+2 X^2 X^2+2 X^2+2
 0  0  0 X^2+2  2 X^2 X^2 X^2+2 X^2+2 X^2  2  2 X^2+2 X^2+2 X^2  0  0  2  0  0  2 X^2 X^2 X^2+2 X^2 X^2 X^2+2 X^2+2

generates a code of length 28 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+55x^24+272x^25+508x^26+880x^27+700x^28+880x^29+472x^30+272x^31+29x^32+12x^34+12x^36+3x^40

The gray image is a code over GF(2) with n=224, k=12 and d=96.
This code was found by Heurico 1.16 in 0.078 seconds.