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

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+38x^79+213x^80+76x^81+236x^82+278x^83+378x^84+248x^85+258x^86+98x^87+174x^88+28x^89+15x^90+2x^91+2x^92+2x^94+1x^154

The gray image is a code over GF(2) with n=672, k=11 and d=316.
This code was found by Heurico 1.16 in 0.75 seconds.