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

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

Homogenous weight enumerator: w(x)=1x^0+54x^74+101x^76+16x^77+146x^78+352x^79+708x^80+400x^81+142x^82+53x^84+38x^86+30x^88+4x^90+2x^92+1x^152

The gray image is a code over GF(2) with n=640, k=11 and d=296.
This code was found by Heurico 1.16 in 0.672 seconds.