The generator matrix

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

generates a code of length 28 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+55x^24+272x^25+508x^26+880x^27+700x^28+880x^29+472x^30+272x^31+29x^32+12x^34+12x^36+3x^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 0.094 seconds.