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

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

Homogenous weight enumerator: w(x)=1x^0+312x^71+1702x^72+2994x^73+5632x^74+7266x^75+11452x^76+12148x^77+16079x^78+15436x^79+16507x^80+13070x^81+11435x^82+6856x^83+5351x^84+2414x^85+1400x^86+580x^87+235x^88+88x^89+71x^90+14x^91+15x^92+6x^93+7x^94+1x^104

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 174 seconds.