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  X  1  1  1  1  X  1  1  1  1  0  1  1  1  2  1  0  X  1  1  1  1  X 2X  2  X  0 2X  1  1  1  X
 0  X  0  X  0 2X 3X  X 2X+2 3X+2 2X+2 X+2 2X+2  2 X+2 X+2  0  2  X X+2  X  0 2X 3X 3X+2  2 3X+2 X+2  2 2X 3X 2X  2 X+2  0 3X 3X 2X+2 3X 3X 2X+2 X+2 2X+2 2X+2 2X 3X 2X+2 X+2 3X+2  0  X 2X+2 2X+2 3X 3X+2 X+2  0 2X+2 3X+2  0 X+2  X  X 2X X+2 2X  0  0  2  X  0 3X+2 3X  X  2 2X  2  X  X  X  X  0  2  X 3X
 0  0  X  X  2 X+2 3X+2 2X+2 2X+2 X+2  X  0 2X X+2 3X 2X+2  0 3X  X 2X+2 X+2  X 2X+2  2 X+2 3X+2  0 3X  0 3X+2  0 2X  2 2X+2  X 3X 2X+2 3X X+2 2X  2  X  2  X  X  X 2X  2 3X  0 3X+2 2X 3X+2 2X 2X  0 2X+2 3X+2  0 2X+2 X+2  0 2X+2  X X+2 X+2 3X+2  X 3X+2  0 3X+2 3X+2  X 3X X+2 X+2  X 2X  2 2X  0 3X+2 2X 2X+2 3X+2
 0  0  0 2X  0  0 2X  0 2X  0 2X 2X 2X 2X  0 2X  0 2X  0 2X  0  0  0  0 2X  0  0 2X 2X 2X 2X 2X 2X  0 2X  0 2X  0  0 2X  0 2X  0  0 2X 2X  0  0  0 2X 2X  0 2X 2X  0 2X 2X  0  0 2X  0  0 2X  0 2X  0 2X 2X 2X 2X  0 2X  0  0 2X 2X  0  0 2X  0  0  0 2X 2X  0
 0  0  0  0 2X 2X 2X 2X 2X 2X  0  0  0 2X  0 2X 2X 2X  0  0 2X 2X  0  0  0  0 2X 2X 2X  0 2X  0  0  0 2X 2X 2X  0  0  0 2X  0  0 2X  0 2X 2X 2X 2X 2X  0  0  0  0  0 2X  0 2X 2X 2X  0 2X  0  0  0  0 2X 2X  0 2X 2X 2X 2X 2X  0  0 2X  0 2X 2X 2X 2X  0 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+398x^80+56x^81+572x^82+312x^83+484x^84+544x^85+476x^86+320x^87+506x^88+40x^89+292x^90+8x^91+44x^92+20x^94+6x^96+16x^98+1x^144

The gray image is a code over GF(2) with n=680, k=12 and d=320.
This code was found by Heurico 1.16 in 27.1 seconds.