The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2+2  1  1 X+2  1  1  0  1  1 X^2+X  1  1 X^2+2  1  1 X+2  1  1  0  1  1 X^2+X  1  1 X+2  1  1 X^2+2  1  2  1  1 X^2  1  1 X^2+X  1  1  1 X+2  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0 X^2+X+2  X X^2+2  0 X^2+X X^2+2 X+2  1  1  1  1  1  1  1  1  1  1
 0  1 X+1 X^2+X X^2+1  1 X^2+X+3 X^2+2  1 X+2  3  1  0 X+1  1 X^2+X X^2+1  1 X^2+2 X^2+X+3  1 X+2  3  1  0 X+1  1 X^2+X X^2+1  1 X+2 X^2+X+3  1  3 X^2+2  1  2  1 X+1 X^2+X  1 X^2+X+3 X^2+1  1 X^2 X+2  3  1 X^2+X+2  0  X X^2+2  0 X^2+X X^2+2 X+2  0 X^2+X X^2+2 X+2  2 X^2+X+2 X^2  X  1  1  1  1  1  1  1  1 X+3 X^2+X+1 X^2+3  1 X+1 X^2+1 X+3 X+1  3 X+3
 0  0  2  0  0  0  0  2  2  2  2  2  0  0  0  2  2  2  2  2  2  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  0  0  0  2  2  2  0  0  2  0  2  2  2  2  0  0  2  0  0  2  2  0  0  0  2  2  0  2  2  2  0  0  2  2  0  0  2  2  2  0  2  0  0  2  2  2
 0  0  0  2  0  2  2  2  2  0  2  0  0  0  2  0  0  2  2  2  0  2  2  0  2  0  0  0  2  2  2  0  2  2  0  0  2  2  2  2  2  2  0  0  0  0  0  0  0  2  2  0  2  0  2  0  0  2  2  0  0  2  0  2  2  0  2  0  0  2  0  2  0  0  2  2  2  2  2  2  0  2
 0  0  0  0  2  0  2  2  2  2  0  2  2  0  2  0  2  0  0  2  0  2  0  2  2  2  2  2  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0  0  0  0  0  2  0  0  2  2  0  2  0  2  2  0  2  0  2  0  0  0  0  0  2  2  2  0  2  2  0  2  2  0  0  0  2  2  2

generates a code of length 82 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+264x^78+64x^79+270x^80+64x^81+720x^82+64x^83+270x^84+64x^85+264x^86+1x^100+1x^112+1x^116

The gray image is a code over GF(2) with n=656, k=11 and d=312.
This code was found by Heurico 1.16 in 0.438 seconds.