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

generates a code of length 82 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+320x^73+1543x^74+3216x^75+6253x^76+9946x^77+15115x^78+21422x^79+26649x^80+29704x^81+33263x^82+30584x^83+27230x^84+21180x^85+15374x^86+9480x^87+5359x^88+2990x^89+1420x^90+536x^91+333x^92+126x^93+37x^94+26x^95+25x^96+6x^97+6x^100

The gray image is a code over GF(2) with n=656, k=18 and d=292.
This code was found by Heurico 1.16 in 688 seconds.