The generator matrix

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

generates a code of length 85 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+91x^78+706x^79+1754x^80+2482x^81+2794x^82+3544x^83+3366x^84+4044x^85+3468x^86+3292x^87+2534x^88+1966x^89+1224x^90+726x^91+370x^92+152x^93+78x^94+78x^95+43x^96+20x^97+16x^98+6x^99+4x^100+8x^101+1x^102

The gray image is a code over GF(2) with n=680, k=15 and d=312.
This code was found by Heurico 1.16 in 14.6 seconds.