The generator matrix

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

generates a code of length 80 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+50x^74+206x^75+306x^76+358x^77+392x^78+552x^79+513x^80+572x^81+327x^82+278x^83+227x^84+138x^85+57x^86+48x^87+28x^88+20x^89+5x^90+4x^91+13x^92+1x^134

The gray image is a code over GF(2) with n=640, k=12 and d=296.
This code was found by Heurico 1.16 in 0.89 seconds.