The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X X^2+2  0  1  2 X^2  1  1  1  1  X
 0  X  0  X  0  2 X^2+X X^2 X^2+X X^2 X^2 X^2+2 X+2 X^2+X+2 X^2+X  X X^2+2  X  X  X X+2 X^2+2 X^2  2  0 X+2 X^2+2  X
 0  0  X  X X^2+2 X^2+X+2 X^2+X X^2+2  2  0  X X^2+X X^2+X  X X^2+2 X^2 X+2 X+2 X^2+X+2 X^2+X+2  X  X  X X+2 X^2+X  X X^2+X+2  X
 0  0  0  2  0  0  0  2  2  2  2  2  0  2  0  2  0  2  2  0  0  0  0  2  0  0  0  2
 0  0  0  0  2  2  0  0  2  2  0  2  2  2  0  2  2  2  0  0  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+219x^24+64x^25+764x^26+448x^27+1169x^28+448x^29+680x^30+64x^31+201x^32+28x^34+6x^36+3x^40+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 0.61 seconds.