The generator matrix

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

generates a code of length 78 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+298x^70+1438x^71+3001x^72+5824x^73+7364x^74+10608x^75+13296x^76+15716x^77+15947x^78+15666x^79+13815x^80+11214x^81+7299x^82+4892x^83+2315x^84+1316x^85+475x^86+340x^87+147x^88+38x^89+39x^90+16x^91+4x^93+2x^98+1x^100

The gray image is a code over GF(2) with n=624, k=17 and d=280.
This code was found by Heurico 1.16 in 174 seconds.