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

generates a code of length 82 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+20x^77+99x^78+152x^79+262x^80+350x^81+370x^82+376x^83+179x^84+56x^85+51x^86+64x^87+61x^88+6x^89+1x^156

The gray image is a code over GF(2) with n=656, k=11 and d=308.
This code was found by Heurico 1.16 in 0.688 seconds.