The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  0  1  1  2 X^2+2  1  1  X  1  1  X X^2  1
 0  X  0 X^2+X+2  2 X^2+X  0  X X^2 X^2+X+2 X^2+2 X+2 X^2+2  X X^2+2  X X^2+X+2  X  X  X X^2+X  2 X^2+X X^2+X  2 X^2+X  2 X^2+X+2
 0  0 X^2+2  0  2 X^2+2 X^2+2 X^2 X^2 X^2  2 X^2 X^2 X^2+2  0  2  0  2  0 X^2+2  0 X^2 X^2+2 X^2+2  0  2 X^2  2
 0  0  0 X^2+2 X^2+2 X^2 X^2+2  2  0  0 X^2+2 X^2+2 X^2  2  2  2  2 X^2 X^2+2 X^2  0  2 X^2+2 X^2+2 X^2+2  2 X^2+2  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+46x^24+210x^25+235x^26+296x^27+488x^28+342x^29+196x^30+152x^31+37x^32+22x^33+16x^34+4x^36+2x^37+1x^42

The gray image is a code over GF(2) with n=224, k=11 and d=96.
This code was found by Heurico 1.16 in 0.047 seconds.