The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+272x^71+1405x^72+3478x^73+5827x^74+9734x^75+14376x^76+21622x^77+26342x^78+31472x^79+32741x^80+32194x^81+26231x^82+21778x^83+14795x^84+9556x^85+5109x^86+2806x^87+1421x^88+592x^89+216x^90+92x^91+23x^92+26x^93+18x^94+2x^95+6x^96+4x^97+4x^99+1x^102

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 707 seconds.