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  X  0  X  0  X  2  1  1  2  X  X  X  1  1  1  1  1  1  X  0  X  0  1  1  1  X  2  X  2  1  X  X  X  X  1  1  1  1  2  2  0  0  2  X  X  0  X  0  X  2  1  1  X  1  1  X  1  1  X  X
 0  X  0 X+2  2 X+2  2  X  0 X+2  0 X+2  2  X  2  X  0 X+2  0 X+2  2  X  2  X X+2  X X+2  X  X  X  0 X+2  X  X  0  2  2  X  0 X+2  2  X X+2  X X+2  X  0  2  0  X  X  X  X  2  0  2  0  2 X+2  X X+2  X  0  2  2  0  2  0  2  2 X+2  X  X  X  0  0  2  2  2  0 X+2 X+2  0  0
 0  0  2  2  2  0  0  2  0  0  2  2  2  2  0  0  0  0  2  2  2  2  0  0  0  2  2  0  2  0  0  0  2  0  2  2  0  0  2  2  2  2  0  2  2  0  0  0  2  2  0  0  2  2  0  0  2  2  0  0  2  2  2  2  2  2  0  0  0  0  0  2  0  2  0  2  0  2  0  0  0  2  2  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+43x^84+10x^86+1x^88+6x^90+3x^92

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 0.407 seconds.