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

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

Homogenous weight enumerator: w(x)=1x^0+38x^84+8x^85+4x^86+6x^87+1x^88+4x^90+2x^95

The gray image is a code over GF(2) with n=336, k=6 and d=168.
This code was found by Heurico 1.16 in 0.306 seconds.