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  X  X  1  1  1  1  1  1  1  1  1  1  1  1  1 X^2  1 X^2 X^2  X  1
 0 X^2+2  0 X^2+2  0 X^2+2  0 X^2+2  0 X^2+2  0 X^2+2  0 X^2+2  0 X^2+2  0 X^2+2  0 X^2+2  0 X^2+2  0 X^2+2  2 X^2  2 X^2  2 X^2  2 X^2  0 X^2+2  2 X^2  2 X^2  2 X^2  0 X^2+2  2 X^2 X^2  2  2 X^2  0 X^2  2 X^2  2 X^2+2  2 X^2  0 X^2+2  2 X^2  2 X^2  2 X^2 X^2+2 X^2+2  0 X^2+2  0 X^2+2  0 X^2+2  0  0  2 X^2+2  0 X^2  2 X^2+2 X^2+2 X^2+2  2  0  0
 0  0  2  0  0  0  2  0  0  0  0  0  2  0  2  0  0  2  0  2  0  2  0  2  2  2  2  2  2  2  2  2  2  2  2  2  0  0  0  0  2  2  2  2  0  0  0  0  2  2  0  0  2  2  0  0  2  2  2  2  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  0  2  2  2  2  2  2  2  0  0
 0  0  0  2  0  0  0  2  0  0  0  0  0  2  0  2  2  2  2  2  2  2  2  2  2  0  2  0  2  0  2  0  2  0  0  2  2  2  0  0  2  0  0  2  2  2  0  0  2  2  0  0  0  0  2  2  2  0  0  2  2  2  0  0  0  0  0  0  2  2  2  0  2  2  0  0  0  0  2  0  2  2  0  0  0
 0  0  0  0  2  0  2  0  0  2  2  2  2  2  0  2  2  0  2  0  0  2  0  2  2  0  2  0  0  2  0  2  0  2  0  2  0  2  0  2  0  2  0  0  0  2  2  0  2  0  2  2  2  0  2  0  2  0  2  2  0  2  0  0  0  0  0  2  2  0  0  2  0  2  0  2  0  2  2  0  2  2  2  0  0
 0  0  0  0  0  2  0  2  2  2  2  0  2  0  2  2  0  0  2  2  2  2  0  0  0  0  2  2  2  2  0  0  0  0  0  0  0  0  0  0  2  2  2  2  0  0  2  2  2  0  0  2  2  2  2  2  0  0  0  2  2  2  2  0  0  2  0  2  0  0  0  0  2  2  2  0  0  2  0  2  0  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+17x^80+18x^81+61x^82+94x^83+118x^84+420x^85+114x^86+92x^87+50x^88+10x^89+14x^90+6x^91+6x^92+1x^94+1x^98+1x^158

The gray image is a code over GF(2) with n=680, k=10 and d=320.
This code was found by Heurico 1.16 in 0.703 seconds.