The generator matrix

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

generates a code of length 83 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+102x^76+844x^77+1510x^78+2462x^79+2631x^80+3570x^81+3650x^82+4150x^83+3449x^84+3448x^85+2303x^86+2008x^87+1054x^88+786x^89+362x^90+184x^91+103x^92+56x^93+46x^94+10x^95+12x^96+16x^97+8x^98+2x^99+1x^102

The gray image is a code over GF(2) with n=664, k=15 and d=304.
This code was found by Heurico 1.16 in 14.6 seconds.