The generator matrix

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

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+18x^22+88x^23+11x^24+8x^25+1x^26+1x^34

The gray image is a code over GF(2) with n=184, k=7 and d=88.
This code was found by Heurico 1.16 in 0 seconds.