The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+480x^76+1816x^77+3084x^78+4370x^79+5590x^80+6734x^81+7306x^82+7980x^83+6800x^84+6602x^85+5286x^86+4012x^87+2615x^88+1440x^89+806x^90+348x^91+102x^92+70x^93+54x^94+22x^95+4x^96+10x^97+4x^99

The gray image is a code over GF(2) with n=664, k=16 and d=304.
This code was found by Heurico 1.16 in 47.5 seconds.