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

generates a code of length 83 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 79.

Homogenous weight enumerator: w(x)=1x^0+166x^79+92x^80+242x^81+168x^82+756x^83+187x^84+212x^85+24x^86+126x^87+39x^88+26x^89+8x^91+1x^156

The gray image is a code over GF(2) with n=664, k=11 and d=316.
This code was found by Heurico 1.16 in 0.703 seconds.