The generator matrix

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

generates a code of length 81 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+86x^77+292x^78+294x^79+294x^80+258x^81+232x^82+212x^83+192x^84+86x^85+74x^86+22x^87+1x^90+2x^97+1x^112+1x^114

The gray image is a code over GF(2) with n=648, k=11 and d=308.
This code was found by Heurico 1.16 in 0.625 seconds.