The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X 2X  1  1  1  2  1
 0  X  0  X 2X  0 X+2 X+2  2 2X+2 X+2  2  2 3X+2 3X  X X+2  X  2 3X+2 X+2 2X  2
 0  0  X  X  2 X+2 X+2  0 2X+2  0 2X  X 3X+2 3X+2  X  0 2X 2X+2 3X 2X+2 2X+2  2 3X+2
 0  0  0 2X 2X 2X  0 2X  0 2X  0  0 2X 2X  0 2X 2X  0 2X  0  0  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+191x^20+160x^21+484x^22+448x^23+422x^24+160x^25+136x^26+41x^28+4x^30+1x^40

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.