The generator matrix

 1  0  0  1  1  1  0  1  1  1 X+2 X^2+X  1 X^2+2  1  1  2  1  X  1  1  1 X^2+X+2  1 X^2 X^2+2  1 X^2
 0  1  0  0 X^2+3 X^2+1  1 X+2 X+3  2  1  2  1  1 X+2 X^2+X+3 X^2+X+2 X^2+X  1 X^2 X^2+3 X^2  1 X^2+3  1  1  1 X^2
 0  0  1 X+1 X+1  0 X^2+X+1 X^2+X+2 X+3 X^2+1  1  1  X X^2+X X^2+1 X^2  1  2  X X+2  1 X+3 X^2 X^2+1  2 X^2+X+2  0  1
 0  0  0 X^2 X^2+2  2 X^2  2 X^2+2 X^2 X^2+2  0  2  0  0 X^2+2  2 X^2 X^2 X^2+2  0  2  2 X^2+2  2 X^2+2  0  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+469x^24+928x^25+2170x^26+2864x^27+3490x^28+3056x^29+2110x^30+784x^31+407x^32+48x^33+38x^34+14x^36+2x^38+3x^40

The gray image is a code over GF(2) with n=224, k=14 and d=96.
This code was found by Heurico 1.16 in 4.7 seconds.