The generator matrix

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

generates a code of length 79 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+304x^71+1511x^72+3406x^73+5078x^74+7916x^75+10369x^76+13346x^77+15077x^78+17066x^79+15382x^80+13912x^81+10277x^82+7606x^83+4546x^84+2754x^85+1380x^86+622x^87+304x^88+102x^89+55x^90+38x^91+15x^92+1x^94+4x^98

The gray image is a code over GF(2) with n=632, k=17 and d=284.
This code was found by Heurico 1.16 in 169 seconds.