The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0 X^2+2  0 X^2+2  0 X^2+2  2 X^2  0 X^2+2  0 X^2+2  0 X^2+2  2 X^2  0 X^2+2  2 X^2  2 X^2  2 X^2  0  2 X^2+2  0
 0  0  2  0  0  0  2  0  0  2  2  2  0  2  2  2  2  0  2  2  0  2  0  0  2  2  0  0
 0  0  0  2  0  0  0  2  2  2  2  2  2  0  2  0  2  2  0  0  2  2  0  0  0  2  0  0
 0  0  0  0  2  2  2  2  2  0  0  2  0  2  2  0  2  2  0  2  2  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+3x^24+16x^25+8x^26+16x^27+424x^28+16x^29+8x^30+16x^31+3x^32+1x^56

The gray image is a code over GF(2) with n=224, k=9 and d=96.
This code was found by Heurico 1.16 in 0.016 seconds.