The generator matrix

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

generates a code of length 80 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+374x^73+1642x^74+2810x^75+4576x^76+6078x^77+6318x^78+7524x^79+8141x^80+7052x^81+6552x^82+5122x^83+3974x^84+2638x^85+1438x^86+756x^87+294x^88+114x^89+82x^90+40x^91+6x^92+4x^95

The gray image is a code over GF(2) with n=640, k=16 and d=292.
This code was found by Heurico 1.16 in 47.7 seconds.