The generator matrix

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

generates a code of length 85 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+183x^80+364x^81+310x^82+484x^83+528x^84+496x^85+430x^86+512x^87+280x^88+272x^89+146x^90+44x^91+28x^92+8x^96+4x^97+2x^110+2x^112+1x^116+1x^124

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 0.781 seconds.