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

generates a code of length 81 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+65x^76+32x^77+288x^78+256x^79+252x^80+448x^81+128x^82+256x^83+62x^84+32x^85+224x^86+2x^88+1x^92+1x^144

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 0.656 seconds.