The generator matrix

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

generates a code of length 28 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+376x^22+1776x^23+6265x^24+14720x^25+30216x^26+47660x^27+59042x^28+48692x^29+31180x^30+14536x^31+5483x^32+1544x^33+496x^34+92x^35+54x^36+4x^37+4x^38+3x^40

The gray image is a code over GF(2) with n=224, k=18 and d=88.
This code was found by Heurico 1.16 in 190 seconds.