The generator matrix

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

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+113x^20+294x^21+428x^22+478x^23+345x^24+218x^25+127x^26+26x^27+5x^28+8x^29+4x^30+1x^34

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 0.016 seconds.