The generator matrix

 1  0  0  1  1  1  0 X^2+2 X^2+2 X^2+2  1  1  1  1 X^2+X  1 X^2+X  1  X  1  1 X^2+X+2 X^2+X+2  X  1  1  1  1  1  0  1  1  1  1  2  1 X^2+X  1  2  1  X  1  X X^2  1  1 X^2+2  1 X^2+X  1  1  1 X^2+2  1  1  1 X^2+X X+2  1  1 X^2+2  2  1 X^2+X+2  2  1  2  1  1  X  1  1  1 X+2  1 X^2+X  2 X+2  2  1
 0  1  0  0 X^2+1 X^2+3  1  X  1  1 X^2+2 X^2 X^2+3 X^2+3 X^2+2 X+1  1  X  1 X^2+X X^2+X+1 X+2  1  1 X^2+X+2  X X^2+X+1  3 X+3 X^2+X+2 X+2 X+1 X^2+X+1 X^2+2 X^2 X^2  1 X^2+X+1  1 X+1  1  0 X^2+X  1 X^2+1 X^2+X+2  2  0 X+2 X+2 X^2+X  1  1 X^2+X+2 X^2+2 X^2+3  1  0 X^2+X+1 X^2+3  1  1  2  1  1  3  1 X^2+X+2 X^2+X+2  1 X^2+2 X+3 X^2+2  1  2  1  1  1  0  0
 0  0  1 X+1 X^2+X+1 X^2 X^2+X+1  1  X  3  X X^2+3  1 X^2+X  1 X^2+X X^2+1 X^2+3 X^2  0  3  1 X+1 X^2+X+2 X+2 X+1 X^2 X^2+X+3 X^2+X+3  1 X^2+X+2 X^2 X^2+1 X^2+X+3  1  1 X^2+X+3 X^2+X+1  2 X^2+X X+2 X+2  1  3  0  1  1 X^2+X  1  1  0 X+3 X^2+X X+1  0 X^2+3  1  1  2 X^2+1 X+3  3 X^2+X+1 X^2  2  X X^2+X+2 X+1 X+3  0 X+2 X+3  3  3 X^2+1 X^2+X+2 X^2+1  1  1  0
 0  0  0 X^2 X^2  0 X^2 X^2+2 X^2  2 X^2  0  2 X^2+2 X^2+2  0 X^2 X^2 X^2+2  2 X^2 X^2+2  2  0  2 X^2+2 X^2+2 X^2+2  2  0 X^2+2  0  0  0  2 X^2 X^2+2 X^2 X^2 X^2 X^2  2  2 X^2 X^2+2 X^2+2 X^2 X^2+2  0  2 X^2  2  2  0 X^2+2 X^2+2  2  2  2  0  0  0  2 X^2  2  2 X^2+2 X^2  2  0  0 X^2+2 X^2+2 X^2  2 X^2  0  0  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+178x^74+698x^75+1412x^76+1522x^77+1881x^78+1956x^79+2041x^80+1692x^81+1662x^82+1108x^83+827x^84+520x^85+403x^86+246x^87+117x^88+36x^89+49x^90+22x^91+1x^92+6x^93+2x^95+1x^96+3x^98

The gray image is a code over GF(2) with n=640, k=14 and d=296.
This code was found by Heurico 1.16 in 3.66 seconds.