The generator matrix

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

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+550x^77+1718x^78+2960x^79+4592x^80+5570x^81+6884x^82+7508x^83+7590x^84+6838x^85+6466x^86+5282x^87+3919x^88+2642x^89+1635x^90+678x^91+356x^92+164x^93+90x^94+46x^95+22x^96+12x^97+7x^98+6x^99

The gray image is a code over GF(2) with n=672, k=16 and d=308.
This code was found by Heurico 1.16 in 47.5 seconds.