The generator matrix

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

generates a code of length 28 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 23.

Homogenous weight enumerator: w(x)=1x^0+272x^23+1710x^24+4172x^25+7680x^26+11298x^27+14784x^28+12218x^29+7706x^30+3644x^31+1567x^32+376x^33+84x^34+18x^35+2x^37+2x^38+2x^40

The gray image is a code over GF(2) with n=224, k=16 and d=92.
This code was found by Heurico 1.16 in 13.5 seconds.