The generator matrix

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

generates a code of length 80 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+272x^72+1484x^73+3225x^74+5720x^75+7807x^76+10792x^77+13194x^78+15414x^79+15629x^80+15158x^81+13405x^82+11324x^83+7731x^84+4956x^85+2484x^86+1356x^87+591x^88+290x^89+130x^90+52x^91+32x^92+8x^93+8x^94+6x^95+2x^98+1x^104

The gray image is a code over GF(2) with n=640, k=17 and d=288.
This code was found by Heurico 1.16 in 210 seconds.