The generator matrix

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

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+132x^24+192x^25+608x^26+576x^27+1090x^28+576x^29+608x^30+192x^31+109x^32+6x^36+6x^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.