The generator matrix

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

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+174x^20+128x^21+576x^22+256x^23+641x^24+128x^25+128x^26+13x^28+2x^32+1x^36

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 0.031 seconds.