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

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

Homogenous weight enumerator: w(x)=1x^0+403x^80+32x^81+462x^82+384x^83+658x^84+480x^85+526x^86+320x^87+366x^88+64x^89+250x^90+86x^92+42x^94+21x^96+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 17.5 seconds.