The generator matrix

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

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+158x^76+332x^77+501x^78+480x^79+469x^80+382x^81+469x^82+396x^83+382x^84+268x^85+152x^86+44x^87+23x^88+10x^89+11x^90+8x^91+2x^92+2x^98+4x^104+1x^110+1x^112

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 0.672 seconds.