The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X X^2+2  1  X  1  1  1  2  X  1  1 X^2  1
 0  X  0  X  2  0 X^2+X X^2+X+2  0  2 X+2 X+2  0 X^2+2 X^2+X+2 X^2+2 X^2 X+2  X X+2  X X^2+X+2  X X+2 X^2+2 X^2+2 X^2+2 X^2+2
 0  0  X  X  0 X^2+X+2 X^2+X  2 X^2 X^2+X+2 X^2+X+2 X^2 X^2+2  X X^2 X+2  X X+2 X^2+X+2  0 X^2+X  2 X^2+X X^2+2 X^2  0  0 X^2+X
 0  0  0 X^2 X^2+2 X^2  2 X^2 X^2  0 X^2 X^2+2  0 X^2+2  0  2 X^2+2  0 X^2 X^2+2  2  2 X^2+2 X^2  0  2  0 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+194x^24+252x^25+476x^26+736x^27+849x^28+772x^29+350x^30+236x^31+149x^32+48x^33+20x^34+4x^35+6x^36+2x^38+1x^44

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 0.156 seconds.