The generator matrix

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

generates a code of length 23 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+300x^20+128x^21+464x^22+256x^23+548x^24+128x^25+144x^26+76x^28+3x^32

The gray image is a code over GF(2) with n=184, k=11 and d=80.
This code was found by Heurico 1.16 in 12.4 seconds.