The generator matrix

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

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+120x^73+702x^74+1448x^75+2475x^76+2678x^77+3675x^78+3730x^79+3829x^80+3642x^81+3442x^82+2488x^83+2058x^84+1116x^85+737x^86+280x^87+190x^88+66x^89+31x^90+24x^91+3x^92+10x^93+4x^94+14x^95+4x^96+1x^98

The gray image is a code over GF(2) with n=640, k=15 and d=292.
This code was found by Heurico 1.16 in 12.4 seconds.