The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+188x^75+722x^76+1138x^77+1743x^78+1674x^79+2417x^80+1902x^81+1716x^82+1462x^83+1264x^84+698x^85+616x^86+358x^87+267x^88+98x^89+58x^90+14x^91+14x^92+20x^93+10x^94+1x^96+2x^100+1x^102

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 3.77 seconds.