The generator matrix

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

generates a code of length 80 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+1x^84+10x^85+2x^86+2x^87

The gray image is a code over GF(2) with n=320, k=4 and d=168.
This code was found by Heurico 1.16 in 0.251 seconds.