The generator matrix

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

generates a code of length 81 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+19x^76+386x^77+483x^78+582x^79+498x^80+596x^81+310x^82+434x^83+245x^84+260x^85+114x^86+60x^87+36x^88+34x^89+15x^90+12x^91+4x^93+4x^94+1x^102+1x^104+1x^106

The gray image is a code over GF(2) with n=648, k=12 and d=304.
This code was found by Heurico 1.16 in 0.797 seconds.