The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 2X  1  1  1  1  1  1  1  1  0  X  1  1  0 2X  1  1  1
 0  X  0 3X+2 2X X+2  0  X  2 X+2 2X+2  X  2 3X  2 X+2  0 3X+2  2 3X+2 2X X+2 2X  X  0  X  0  X 2X+2 3X  X  2  2 X+2 X+2 2X+2  2 3X  X 2X+2 3X 2X+2  2  X 3X 2X+2 X+2 2X+2 X+2 3X+2  0  0  X 3X 2X  0 2X X+2 3X+2 X+2 3X+2 2X+2 2X 2X  0 2X+2 2X+2  0 2X+2  2  2  2  X 3X+2 3X+2 3X  X  X 2X  0 2X
 0  0 2X+2  0  0 2X+2  2  2  2 2X 2X+2 2X 2X  2 2X 2X+2  0  2 2X  0 2X+2  2  2  0 2X 2X 2X  2 2X+2  0 2X+2 2X+2  0 2X  2  0  2  0 2X+2 2X+2 2X+2  2  2 2X 2X+2  0  0  0 2X 2X+2 2X  0 2X  2 2X  2 2X+2  0  2 2X 2X+2 2X 2X+2  0  2 2X 2X 2X+2  2  2  0  0  0 2X 2X+2 2X+2  2  2  2  0  0
 0  0  0 2X+2  2 2X+2  2  0  0  0  2 2X+2  2 2X+2  0  0 2X  0 2X+2  0 2X 2X+2 2X+2 2X+2 2X+2 2X 2X 2X 2X+2  2 2X+2  0  0 2X+2  2  2 2X+2 2X  0 2X 2X  2 2X  0  2 2X+2  2 2X  2  2  2 2X+2  2  2  0 2X 2X+2 2X 2X 2X 2X  0  2  0  0 2X  2 2X 2X+2  2  2 2X  0 2X+2 2X+2  0  2  0  0 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+38x^76+72x^77+154x^78+312x^79+402x^80+368x^81+228x^82+144x^83+101x^84+72x^85+82x^86+56x^87+16x^88+1x^92+1x^152

The gray image is a code over GF(2) with n=648, k=11 and d=304.
This code was found by Heurico 1.16 in 0.657 seconds.