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  1 2X  1  1  1  1  1  1  1  1  2  1  1  1  0  1  X  1
 0  X  0 X+2  2 3X+2 2X+2  X  0 X+2 2X+2 3X X+2 2X  X 2X+2 2X X+2  2  X  0 3X+2 2X+2 3X 2X 3X+2 2X+2  X 2X+2 X+2 2X  X X+2  0  0  X 3X  2 3X+2 2X+2 3X+2  0  0 3X  X  2 3X+2 2X+2 2X+2 3X+2 3X 2X+2  X  X  2  2 3X+2 3X  0 2X 2X  0 3X+2 X+2 2X 3X+2  0 2X 2X  0 X+2 X+2 X+2  2 2X  2 X+2  X  X 3X+2 2X
 0  0 2X+2  0  2  2  0  2  0  0  0  0 2X+2 2X+2 2X+2  2  2 2X 2X+2  2 2X  2 2X 2X 2X 2X 2X 2X 2X+2 2X+2  2 2X+2  0  0 2X+2  2 2X+2 2X+2  0 2X  2  0 2X+2  0 2X  0 2X+2  2 2X+2 2X+2 2X  0  0  2 2X  2  2 2X+2 2X  2 2X  2  0 2X  0 2X 2X 2X  2  2 2X 2X+2  2  2 2X 2X+2  0  0  2 2X+2 2X+2
 0  0  0 2X  0  0  0 2X 2X 2X 2X  0  0 2X 2X 2X  0 2X  0 2X  0  0  0  0 2X 2X 2X  0 2X  0 2X 2X  0  0 2X  0  0 2X  0  0 2X 2X  0 2X 2X  0 2X 2X  0 2X 2X 2X 2X  0 2X  0 2X  0 2X 2X  0  0 2X  0  0  0 2X 2X  0  0 2X 2X 2X 2X  0 2X  0  0 2X 2X 2X
 0  0  0  0 2X  0 2X  0 2X 2X  0 2X 2X 2X 2X  0  0  0 2X 2X  0 2X 2X  0 2X 2X  0 2X  0  0 2X  0  0 2X  0  0 2X 2X 2X  0 2X  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0 2X 2X  0  0  0  0  0 2X 2X  0  0  0 2X 2X  0 2X  0 2X 2X  0  0  0 2X 2X 2X  0 2X  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+28x^76+124x^77+133x^78+236x^79+435x^80+328x^81+319x^82+160x^83+72x^84+100x^85+27x^86+52x^87+8x^88+24x^89+1x^154

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 0.875 seconds.