The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+166x^77+868x^78+1528x^79+1992x^80+3038x^81+3430x^82+3904x^83+3849x^84+3768x^85+3006x^86+2712x^87+1947x^88+1094x^89+615x^90+388x^91+192x^92+118x^93+65x^94+16x^95+26x^96+24x^97+7x^98+12x^99+1x^100+1x^102

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 14.3 seconds.