The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+368x^75+1684x^76+3612x^77+5936x^78+10420x^79+15536x^80+21166x^81+25797x^82+30810x^83+30739x^84+31460x^85+26782x^86+21314x^87+15241x^88+10210x^89+5493x^90+2872x^91+1489x^92+718x^93+235x^94+128x^95+72x^96+32x^97+10x^98+6x^99+4x^100+2x^101+3x^102+2x^103+2x^104

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 791 seconds.