The generator matrix

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

generates a code of length 80 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+236x^71+1511x^72+3182x^73+5949x^74+9946x^75+14847x^76+20838x^77+26543x^78+31554x^79+32202x^80+32220x^81+27159x^82+21596x^83+14594x^84+9124x^85+5554x^86+2680x^87+1384x^88+590x^89+248x^90+108x^91+31x^92+14x^93+17x^94+6x^95+2x^96+2x^98+2x^99+2x^100+2x^104

The gray image is a code over GF(2) with n=640, k=18 and d=284.
This code was found by Heurico 1.16 in 763 seconds.