The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  0  X  1  X  X  1 2X  1  0  X
 0  X  0 X+2  2 3X+2 2X+2  X  0 X+2 2X+2 2X 2X+2  X 3X+2 3X+2 X+2  X  2  X 2X+2  0 3X
 0  0 2X+2  0  2  2 2X  2  0 2X  0  2  2 2X  2 2X+2 2X 2X+2 2X+2  2 2X  2 2X
 0  0  0 2X  0  0 2X  0  0 2X 2X  0  0  0 2X 2X 2X  0 2X  0  0 2X 2X
 0  0  0  0 2X  0  0 2X 2X 2X 2X 2X  0 2X 2X  0 2X  0  0  0  0  0 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+291x^20+64x^21+584x^22+128x^23+707x^24+64x^25+152x^26+49x^28+8x^32

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 3.24 seconds.