The generator matrix

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

generates a code of length 85 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 79.

Homogenous weight enumerator: w(x)=1x^0+172x^79+727x^80+1362x^81+1713x^82+1844x^83+2027x^84+1738x^85+1923x^86+1406x^87+1100x^88+816x^89+654x^90+400x^91+217x^92+154x^93+59x^94+34x^95+13x^96+10x^97+11x^98+3x^104

The gray image is a code over GF(2) with n=680, k=14 and d=316.
This code was found by Heurico 1.16 in 4.14 seconds.