The generator matrix

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

generates a code of length 84 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 79.

Homogenous weight enumerator: w(x)=1x^0+144x^79+722x^80+992x^81+1222x^82+948x^83+1177x^84+788x^85+548x^86+360x^87+446x^88+336x^89+238x^90+108x^91+94x^92+28x^93+24x^94+8x^95+5x^96+1x^100+2x^104

The gray image is a code over GF(2) with n=672, k=13 and d=316.
This code was found by Heurico 1.16 in 1.27 seconds.