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  X  1  1  1  1  1
 0  X X^2+2 X^2+X  0 X^2+X X^2+2 X+2  0 X^2+X X^2+2 X+2  0 X^2+X  2 X^2+X+2 X^2+2 X+2 X^2 X+2 X^2+2 X^2+X X^2+X  0  2  0 X^2  2
 0  0  2  0  0  0  2  2  2  0  0  2  0  2  2  2  0  0  2  2  0  0  2  0  0  2  2  2
 0  0  0  2  0  0  2  2  0  2  2  2  2  0  2  0  0  2  0  0  2  0  0  2  2  2  0  0
 0  0  0  0  2  2  0  0  2  2  2  2  0  2  2  0  0  2  2  2  0  0  0  2  0  0  0  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+18x^24+56x^25+33x^26+168x^27+476x^28+168x^29+27x^30+56x^31+17x^32+3x^34+1x^54

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 0.031 seconds.