The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+446x^77+1942x^78+3490x^79+5213x^80+8148x^81+10697x^82+13406x^83+14875x^84+15420x^85+15025x^86+13222x^87+10425x^88+7628x^89+5068x^90+2920x^91+1678x^92+894x^93+311x^94+174x^95+31x^96+40x^97+13x^98+2x^99+1x^100+2x^103

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 222 seconds.