The generator matrix

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

generates a code of length 23 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+38x^22+176x^23+38x^24+1x^28+1x^30+1x^34

The gray image is a code over GF(2) with n=184, k=8 and d=88.
This code was found by Heurico 1.16 in -1.01e-007 seconds.