The generator matrix

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

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+113x^76+240x^77+630x^78+384x^79+617x^80+408x^81+544x^82+224x^83+490x^84+208x^85+76x^86+64x^87+65x^88+8x^89+10x^90+8x^92+2x^94+2x^98+1x^112+1x^116

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 0.859 seconds.