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

generates a code of length 77 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+280x^69+1404x^70+3144x^71+5107x^72+7500x^73+11134x^74+12976x^75+15877x^76+16332x^77+16233x^78+13394x^79+10617x^80+7590x^81+4684x^82+2366x^83+1414x^84+538x^85+269x^86+118x^87+55x^88+14x^89+17x^90+2x^91+1x^92+2x^93+2x^94+1x^98

The gray image is a code over GF(2) with n=616, k=17 and d=276.
This code was found by Heurico 1.16 in 168 seconds.