The generator matrix

 1  0  0  1  1  1 3X+2 3X  1  1 X+2  1  1 3X+2  0  1  1  2  1  1 2X+2  1  X 3X 2X  1  1  1  1  1  1 3X+2  0  1 3X+2  1 2X+2  1 2X+2 2X+2  1  1  1  1 3X X+2  1 2X+2 2X+2  1  1  1  1  1  X  1  0  1 2X  1  2  1  1  1 3X+2  1  1  1 X+2  X  1 2X 2X+2  1  1 3X+2  1 X+2 X+2  1  X  X 3X X+2  2  1
 0  1  0  0  3 X+1  1  2 3X  3  1  2 X+3  1  X  0 3X+2  1 X+3 3X+1  1 2X+3 X+2  1  1  3 3X+2 3X  1 2X+1 3X  1  1 X+1  2  1  1  2 3X+2  1  2 3X+2  3 2X  1  1  1 3X+2  1 X+3  3  3 2X+2 3X+1  1 X+3 2X 3X+2  1  X  1 3X+3 2X 3X+2 3X  X  0 2X+2  1  2  2 2X+2 2X  2  3 3X+2  1  1  0 X+2  1  1 2X+2  1  1 2X+2
 0  0  1  1  1  0  3  1 3X 3X 2X X+3  3 3X+1  1 X+2 3X+1 3X+2 X+3 3X+2 X+3 2X  1 3X+2 2X+3 X+1 2X+2 3X+3  0 2X+1  X 2X+1  0 X+2  1 2X+2 2X+3 X+2  1 3X+1  2 2X+3 3X+1 X+3  2  1 X+3  1 3X  2 3X 3X+2 3X+1 X+1 2X+3 2X+3  1 X+3 2X+1  0  X X+1 3X  0  1 3X+3 X+3 2X+2 2X  1 2X+3  1  1  0 X+3  1  X 3X+3  1 2X+1  2 2X+3  1 3X+2 2X+3  2
 0  0  0  X 3X 2X 3X  X  2 2X+2  0 X+2 3X 3X+2 3X 2X+2 X+2  2 3X+2 2X 3X  2 X+2  0 X+2 3X 2X+2  0 X+2  2 3X 2X+2 3X 3X  0  X 2X+2  X 2X  2 3X  0 2X  X 3X+2 X+2  2  2  X  X  0 X+2  2  X 2X  2  X  X 2X+2 3X+2 2X  0  0 3X 3X  2 2X 2X+2 3X 2X  2  X  2 X+2 3X+2  0  0 X+2  2 3X+2 X+2  0  2 3X  0  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+152x^79+932x^80+1422x^81+2376x^82+2688x^83+3846x^84+3624x^85+3645x^86+3590x^87+3414x^88+2332x^89+2006x^90+998x^91+917x^92+396x^93+178x^94+122x^95+40x^96+30x^97+30x^98+2x^99+17x^100+4x^101+5x^102+1x^104

The gray image is a code over GF(2) with n=688, k=15 and d=316.
This code was found by Heurico 1.16 in 14.2 seconds.