The generator matrix

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

generates a code of length 81 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+436x^73+1434x^74+3442x^75+5515x^76+8160x^77+10196x^78+12702x^79+15213x^80+16612x^81+15747x^82+13378x^83+10475x^84+7336x^85+4788x^86+3096x^87+1373x^88+730x^89+203x^90+122x^91+55x^92+20x^93+14x^94+10x^95+7x^96+2x^97+2x^98+2x^99+1x^100

The gray image is a code over GF(2) with n=648, k=17 and d=292.
This code was found by Heurico 1.16 in 175 seconds.