The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+118x^80+810x^81+546x^82+664x^83+522x^84+478x^85+208x^86+168x^87+153x^88+188x^89+42x^90+116x^91+37x^92+40x^93+2x^94+1x^96+1x^102+1x^106

The gray image is a code over GF(2) with n=672, k=12 and d=320.
This code was found by Heurico 1.16 in 0.422 seconds.