The generator matrix

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

generates a code of length 84 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+362x^75+1602x^76+3750x^77+6321x^78+10382x^79+14901x^80+21238x^81+25491x^82+30644x^83+31612x^84+31032x^85+27081x^86+21694x^87+14927x^88+10190x^89+5176x^90+3056x^91+1449x^92+648x^93+375x^94+90x^95+51x^96+20x^97+33x^98+10x^99+1x^100+2x^101+3x^102+2x^111

The gray image is a code over GF(2) with n=672, k=18 and d=300.
This code was found by Heurico 1.16 in 753 seconds.