The generator matrix

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

generates a code of length 85 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+600x^77+1626x^78+3490x^79+5611x^80+8538x^81+9531x^82+14152x^83+13972x^84+16488x^85+14260x^86+13772x^87+10100x^88+7968x^89+4811x^90+3360x^91+1393x^92+796x^93+318x^94+162x^95+54x^96+38x^97+12x^98+8x^99+5x^100+4x^101+2x^102

The gray image is a code over GF(2) with n=680, k=17 and d=308.
This code was found by Heurico 1.16 in 205 seconds.