The generator matrix

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

generates a code of length 77 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+156x^71+629x^72+1398x^73+1663x^74+1700x^75+1914x^76+2008x^77+2020x^78+1522x^79+1174x^80+954x^81+570x^82+328x^83+159x^84+106x^85+48x^86+2x^87+9x^88+12x^89+4x^91+1x^92+2x^93+2x^94+1x^96+1x^98

The gray image is a code over GF(2) with n=616, k=14 and d=284.
This code was found by Heurico 1.16 in 3.61 seconds.