The generator matrix

 1  0  1  1 X+2  1  1  1  2  1  1 3X  1  0  1  1  X  1  1  0  1  1  1
 0  1  1 X+2  1 3X+1 2X+3  2  1  X 3X+3  1  2  1 3X+1 X+2  1 2X+3 3X+1  1  1 X+2  3
 0  0  X  0 2X  2 2X+2 3X 3X  X 3X+2 X+2 X+2 X+2  X 3X+2 3X  X  2 2X  2 2X  0
 0  0  0 2X 2X  0 2X  0  0 2X 2X 2X  0  0  0  0  0 2X 2X 2X 2X  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+271x^20+348x^21+1226x^22+488x^23+1191x^24+288x^25+220x^26+24x^27+21x^28+4x^29+10x^30+4x^32

The gray image is a code over GF(2) with n=184, k=12 and d=80.
This code was found by Heurico 1.16 in 0.063 seconds.