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

generates a code of length 85 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+33x^80+168x^81+103x^82+32x^83+376x^84+624x^85+376x^86+32x^87+102x^88+168x^89+30x^90+2x^98+1x^162

The gray image is a code over GF(2) with n=680, k=11 and d=320.
This code was found by Heurico 1.16 in 0.782 seconds.