The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+308x^76+152x^77+576x^78+280x^79+659x^80+208x^81+644x^82+208x^83+633x^84+152x^85+184x^86+24x^87+57x^88+4x^90+2x^92+1x^100+3x^104

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 4.75 seconds.