The generator matrix

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

generates a code of length 84 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+44x^78+134x^79+381x^80+442x^81+396x^82+384x^83+631x^84+468x^85+327x^86+302x^87+292x^88+170x^89+55x^90+12x^91+32x^92+8x^93+7x^94+6x^96+1x^98+2x^110+1x^132

The gray image is a code over GF(2) with n=672, k=12 and d=312.
This code was found by Heurico 1.16 in 0.688 seconds.