The generator matrix

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

generates a code of length 81 over Z4[X]/(X^2+2) 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.