The generator matrix

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

generates a code of length 85 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+66x^82+232x^83+167x^84+192x^85+101x^86+144x^87+52x^88+34x^89+24x^90+4x^91+4x^92+2x^93+1x^130

The gray image is a code over GF(2) with n=680, k=10 and d=328.
This code was found by Heurico 1.16 in 0.453 seconds.