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  0  1  1  1  1  1  1  1  1 2X  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  1  1  1  1  1  1  X  X  0  2  X  0  X  X 2X+2  X  X  X  1  1  1  1  X  1
 0  X  0  X  0  0  X  X  2 X+2  2 X+2  2  2 X+2 X+2  0  0  X  X  0  0  X  X 2X  2  2 X+2 X+2  2  2 X+2 X+2 2X 2X 2X+2 3X 3X+2 2X+2 2X 3X+2 3X 2X+2 2X+2 3X 3X+2 2X 2X 3X+2 3X 2X 2X 3X 3X 2X+2 2X+2 3X+2 3X+2 2X 2X 3X+2 3X+2 2X+2 2X+2 3X 3X  X X+2  X  X  X  X  0 3X+2  X 2X+2  2 2X  0  2 2X  2 X+2  0
 0  0  X  X 2X+2 X+2 3X+2  2  2 X+2 3X 2X 3X+2 2X 3X 2X+2 2X 3X+2 3X 2X+2 3X  2 X+2 2X  X 2X+2  X 3X+2  0  0 X+2  X  2  X 2X 3X 3X 2X 2X+2 X+2 X+2 2X+2 X+2  0 3X+2 2X+2  2 3X  X 2X  0 3X+2  X  2  2  X  0 3X+2 2X+2  X  2 3X 2X 3X+2 X+2  0  X  0  0  X 3X+2 2X+2 X+2 2X+2 X+2  2 2X 3X+2  0  X  2  0 X+2  2

generates a code of length 84 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+48x^81+244x^82+152x^83+209x^84+118x^85+150x^86+48x^87+29x^88+16x^89+5x^90+1x^92+2x^93+1x^138

The gray image is a code over GF(2) with n=672, k=10 and d=324.
This code was found by Heurico 1.16 in 0.421 seconds.