The generator matrix

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

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+133x^20+774x^21+636x^22+1208x^23+492x^24+582x^25+163x^26+84x^27+14x^28+8x^29+1x^30

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 0.047 seconds.