The generator matrix

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

generates a code of length 21 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+3x^20+20x^21+3x^22+4x^25+1x^26

The gray image is a code over GF(2) with n=84, k=5 and d=40.
This code was found by Heurico 1.16 in 0.00179 seconds.