The generator matrix

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

generates a code of length 83 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+150x^77+691x^78+1414x^79+1714x^80+1786x^81+1958x^82+2012x^83+1666x^84+1552x^85+1089x^86+880x^87+610x^88+406x^89+226x^90+72x^91+86x^92+42x^93+6x^94+6x^95+11x^96+6x^98

The gray image is a code over GF(2) with n=664, k=14 and d=308.
This code was found by Heurico 1.16 in 4.05 seconds.