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  2
 0 X^2+2  0 X^2+2  0 X^2+2  0 X^2+2  2 X^2  2 X^2+2 X^2+2 X^2+2  0  2  2 X^2  0  0 X^2 X^2  2
 0  0  2  0  0  2  2  2  2  2  2  0  2  2  2  0  0  0  0  2  2  0  0
 0  0  0  2  2  2  2  0  0  0  2  0  2  0  2  0  2  2  2  0  2  2  0

generates a code of length 23 over Z4[X]/(X^3+2,2X) 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.