The generator matrix

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

generates a code of length 86 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 79.

Homogenous weight enumerator: w(x)=1x^0+584x^79+1950x^80+2982x^81+4512x^82+5808x^83+6466x^84+7196x^85+7565x^86+7276x^87+6248x^88+5086x^89+3983x^90+2702x^91+1665x^92+804x^93+415x^94+160x^95+49x^96+24x^97+29x^98+14x^99+11x^100+4x^101+2x^104

The gray image is a code over GF(2) with n=688, k=16 and d=316.
This code was found by Heurico 1.16 in 51.6 seconds.