The generator matrix

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

generates a code of length 84 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+136x^77+732x^78+1542x^79+2400x^80+2888x^81+3299x^82+4134x^83+3754x^84+3648x^85+3045x^86+2516x^87+1881x^88+1264x^89+687x^90+382x^91+238x^92+100x^93+51x^94+18x^95+25x^96+8x^97+10x^98+4x^100+4x^101+1x^104

The gray image is a code over GF(2) with n=672, k=15 and d=308.
This code was found by Heurico 1.16 in 14.7 seconds.