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

generates a code of length 85 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+146x^81+133x^82+186x^83+313x^84+522x^85+346x^86+168x^87+68x^88+82x^89+33x^90+46x^91+1x^92+2x^93+1x^160

The gray image is a code over GF(2) with n=680, k=11 and d=324.
This code was found by Heurico 1.16 in 0.766 seconds.