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

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

Homogenous weight enumerator: w(x)=1x^0+3x^84+54x^85+3x^86+1x^90+2x^93

The gray image is a code over GF(2) with n=672, k=6 and d=336.
This code was found by Heurico 1.16 in 0.469 seconds.