The generator matrix

 1  0  1  1  1 X+2  1  1 2X+2  1  1 3X  1  1  0  1  1 X+2  1  1 X+2  1  1
 0  1 X+1 X+2  3  1 2X+2 3X+3  1 3X 2X+1  1  0 X+1  1 X+2  3  1  0 X+1  1 3X 2X
 0  0 2X  0 2X  0  0 2X  0  0 2X  0 2X  0 2X 2X  0 2X 2X  0 2X  0 2X
 0  0  0 2X 2X 2X 2X 2X 2X  0  0  0 2X  0  0  0 2X 2X  0 2X  0 2X  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+40x^20+120x^21+264x^22+176x^23+259x^24+120x^25+40x^26+2x^28+2x^32

The gray image is a code over GF(2) with n=184, k=10 and d=80.
This code was found by Heurico 1.16 in 0.015 seconds.