The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+150x^80+676x^81+746x^82+624x^83+474x^84+418x^85+202x^86+232x^87+161x^88+158x^89+97x^90+68x^91+36x^92+24x^93+17x^94+8x^95+1x^96+2x^98+1x^100

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 0.469 seconds.