The generator matrix

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

generates a code of length 81 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+172x^75+774x^76+1098x^77+1870x^78+1664x^79+2190x^80+1736x^81+2114x^82+1294x^83+1326x^84+704x^85+611x^86+368x^87+233x^88+100x^89+65x^90+22x^91+19x^92+10x^93+11x^94+1x^98+1x^100

The gray image is a code over GF(2) with n=648, k=14 and d=300.
This code was found by Heurico 1.16 in 3.91 seconds.