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 X^2+2 X^2+X  0 X^2+X X^2+2 X+2  0 X^2+X X+2 X^2+2  2 X^2+X+2 X^2 X+2  0 X^2+X X+2 X^2+2 X^2+X  0 X+2 X^2+2 X^2+X  0 X+2 X^2+2 X^2+X+2  2 X^2  X  0 X^2+X X^2+2 X+2 X^2+X+2  0 X^2  X X^2+X  2 X+2 X^2 X^2+X+2  2 X^2+2  X  0  2 X^2+X X^2+X+2  0 X^2+X  2 X^2+X+2 X^2+2 X^2+2 X^2 X^2 X+2 X+2  X  X  0 X^2+X  0  2  2 X^2+X X^2+X+2 X^2+X+2  0  2  0 X^2+2 X^2 X^2+2 X^2+X  X X^2  2 X^2+X X^2+X  0
 0  0  2  0  0  0  2  0  0  0  0  2  0  0  2  0  0  2  2  0  2  0  2  0  2  2  2  2  2  2  2  2  0  0  0  0  2  2  2  2  0  2  0  2  2  0  0  2  2  2  0  2  2  2  2  0  0  0  0  0  0  2  2  0  0  0  0  0  0  0  0  0  2  2  2  2  2  0  0  2  0  0  0  2  2
 0  0  0  2  0  0  0  2  0  0  0  0  0  2  0  2  2  2  2  2  2  2  2  2  0  2  0  2  0  2  2  0  2  0  0  2  2  0  2  2  0  0  2  2  2  2  0  2  2  0  2  0  2  0  0  2  0  2  2  0  0  0  0  0  0  2  2  2  0  2  2  2  2  2  0  0  0  2  2  0  2  2  2  0  0
 0  0  0  0  2  0  2  0  0  2  2  2  2  2  0  2  2  0  0  2  2  0  2  0  2  0  2  0  0  2  2  0  2  0  0  2  2  0  2  2  2  2  0  0  0  0  2  0  0  2  2  0  2  2  0  0  0  0  2  2  0  2  0  2  2  2  0  0  2  0  0  2  2  2  2  0  2  2  2  0  0  2  0  2  2
 0  0  0  0  0  2  0  2  2  2  0  2  2  0  2  2  0  0  2  2  0  2  2  0  0  0  2  2  0  2  0  2  2  0  0  0  2  0  2  0  0  2  0  0  2  0  2  0  2  0  2  2  0  2  2  2  2  2  0  0  2  0  0  2  2  0  0  2  0  2  0  2  2  0  0  2  2  0  0  0  0  0  2  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+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 0.797 seconds.