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

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+414x^80+40x^81+540x^82+344x^83+500x^84+544x^85+460x^86+288x^87+538x^88+56x^89+276x^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 27.9 seconds.