The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+704x^20+816x^21+1756x^22+1728x^23+1748x^24+752x^25+576x^26+32x^27+72x^28+4x^30+3x^32

The gray image is a code over GF(2) with n=184, k=13 and d=80.
This code was found by Heurico 1.16 in 0.953 seconds.