The generator matrix

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

generates a code of length 23 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+18x^21+125x^22+77x^24+12x^25+18x^26+2x^28+2x^29+1x^30

The gray image is a code over GF(2) with n=184, k=8 and d=84.
This code was found by Heurico 1.16 in 0.047 seconds.