The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1  1  1  1  X  1  1 X^2  X  1
 0 X^2+2  0  0  2 X^2+2 X^2+2 X^2  0  2  0 X^2 X^2 X^2 X^2 X^2  0  0  2  2 X^2+2  0  2 X^2 X^2+2 X^2 X^2  2
 0  0 X^2+2  0 X^2+2 X^2+2 X^2  2  0 X^2 X^2  0  2 X^2  2 X^2  2 X^2 X^2  0  2  2  2 X^2+2 X^2  2 X^2+2 X^2
 0  0  0 X^2+2 X^2  2 X^2 X^2  2  2 X^2 X^2 X^2+2  2  2 X^2+2 X^2+2  2 X^2+2  2  0  0 X^2+2 X^2 X^2+2 X^2+2  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+41x^24+8x^25+104x^26+184x^27+375x^28+184x^29+72x^30+8x^31+25x^32+16x^34+5x^36+1x^48

The gray image is a code over GF(2) with n=224, k=10 and d=96.
This code was found by Heurico 1.16 in 0.015 seconds.