The generator matrix

 1  0  1  1  2  1  1  1 X+2  1  1 2X+2  X  1  1  1  1  0 2X  1  1 3X+2  1  1 3X  X  1  1  X  1  1  1 3X+2  1  0  1  2  1  1  1  1  2  1  1  1  1 3X+2  1  1  1  1  1  1  1  1  1  1  X  1 2X 3X+2  1 2X  0  X  1  1  1  1  1  1  1  X  1  1 2X  1 3X+2  1 X+2 X+2  1  1  X
 0  1  1 X+2  1 X+3  2  3  1 X+1  X  1  1  0  3 2X+2 2X+1  1  1  X X+3  1 3X+2 3X+1  1  1  2  1  1  0  3 3X  1  2  1 X+2  1 X+2 X+1 3X+3 2X+3  1  1  0 X+3  X  1 3X+1  0 3X+1 2X+3 3X+1  3 3X X+1 2X  X 3X  1  1  1 3X+3  1  X  1 2X+2  2 X+2  0 2X+2  2 3X+2 3X 2X  1  X X+2  1 3X+2  1  1 X+2 3X  1
 0  0  X  0 3X  X 3X 2X  0 2X 3X 3X+2  2 2X+2 2X+2 3X+2 3X+2 X+2 3X 3X+2 3X+2 2X+2 2X+2 2X+2  0  X  2  2 3X+2 X+2 X+2 2X  X  0 2X+2 X+2 2X+2 3X X+2 2X+2  X 2X  0 3X 2X 2X+2 X+2  X X+2 3X  X 3X+2 X+2 X+2  0 3X  X  X  X 3X+2  X X+2  X 3X+2 3X+2 X+2  0 X+2 2X 3X  X 3X+2 3X+2 3X 3X 2X 2X+2 3X+2  2 2X 3X+2 3X+2  0 3X
 0  0  0 2X  0 2X 2X 2X 2X  0  0 2X 2X  0 2X 2X  0  0 2X  0 2X  0 2X  0  0  0 2X  0 2X  0 2X  0 2X 2X 2X  0  0  0  0 2X 2X 2X  0 2X 2X  0  0  0 2X 2X  0 2X  0 2X 2X  0 2X 2X 2X 2X  0  0  0  0  0  0  0 2X 2X  0  0 2X  0 2X 2X 2X  0  0  0  0 2X  0  0 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+535x^80+320x^81+728x^82+296x^83+671x^84+256x^85+472x^86+208x^87+384x^88+64x^89+84x^90+8x^91+45x^92+8x^94+5x^96+4x^98+4x^100+1x^104+2x^112

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 50.1 seconds.