The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+514x^79+1774x^80+3090x^81+4687x^82+5930x^83+6385x^84+7272x^85+7243x^86+7638x^87+6183x^88+5238x^89+3782x^90+2530x^91+1605x^92+834x^93+475x^94+176x^95+83x^96+40x^97+29x^98+12x^99+6x^101+8x^102+1x^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 54 seconds.