The generator matrix

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

generates a code of length 81 over Z4[X]/(X^3+2,2X) 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 4.86 seconds.