The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X  1  2  X  1  1  X  1  1 X^2+2  2  1  1  X  1 X^2
 0  X  0 X^2+X+2 X^2 X^2+X X^2+2  X  2  0 X^2 X^2 X^2+X X^2+X  X X^2+X+2 X^2+X+2 X^2+X+2 X^2+X  X  2  X  X X^2+2 X^2+2 X^2  0 X^2+2
 0  0 X^2+2  0 X^2  0  0  2  0 X^2 X^2  2  2 X^2+2 X^2+2  0 X^2 X^2+2 X^2+2 X^2  2  2  2  0 X^2  2 X^2+2  2
 0  0  0 X^2+2  0  0  2 X^2 X^2 X^2 X^2+2 X^2  2 X^2+2  2 X^2  0 X^2 X^2 X^2 X^2  2 X^2+2  2 X^2 X^2+2 X^2  2
 0  0  0  0  2  2  2  2  0  0  2  2  0  2  2  2  2  2  0  2  2  0  2  0  0  0  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+305x^24+64x^25+658x^26+448x^27+1189x^28+448x^29+652x^30+64x^31+204x^32+34x^34+27x^36+2x^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 47.2 seconds.