The generator matrix

 1  0  0  1  1  1 3X+2 3X  1  1 X+2  1  1  2  X 3X  1  1  1  1  0 2X+2  1  1  1  1  1 2X+2  1 3X+2 2X+2 3X  X  1  1  1  X  1  1 3X 2X 2X+2  2  1  1  2  1 3X+2  1  1  1  1  1  1  1  1 3X  1  1  1  1 2X 3X+2 3X+2  0  X  1  1 2X+2 2X  X  2  1  0 3X+2  0  1  1 3X  2  X  1  1
 0  1  0  0  3 X+1  1  2 3X  3  1  2 X+3  1  1 3X+2 3X+2  0 2X+1 X+3  1 3X X+1 2X+3  2  2 3X 2X+2 3X+3  1  1  1  1 2X+3 2X 3X  1 3X+2  1 2X+2  1  1  1  0 X+1 3X  3  1  1 3X 2X+1 3X+2 X+1 3X+3  0 2X+2  1 2X+1 3X+1 3X+1 X+3  1  1 2X+2  1  1  X X+2  1  0  1  1 3X+3  1  1 2X 3X+2 3X+1  1  1 2X+2 2X+3  0
 0  0  1  1  1  0  3  1 3X 3X 2X X+3  3 3X+2 3X+1  1 3X+1 3X+2 2X+2 X+3 X+3  1 X+2 X+1 3X+2  0 2X+1  1 3X+1  1  2 2X+2 X+3 2X X+2 X+1  1  1 3X+3  1 2X+3 3X X+3 3X+3 X+2  1 2X+1 3X 2X+2 X+2  0 2X+2 3X X+3  1 2X X+2 3X+1  0 2X+3 3X+3 2X+1 2X+1  1 2X+1 2X X+3 X+1 X+2  1 2X+3  0  1 2X 3X  1 2X+1  2 3X+2 3X+3  1 2X+1  0
 0  0  0  X 3X 2X 3X  X  2 2X+2  0 X+2 3X  2 3X+2 3X X+2 2X+2  0 3X+2 X+2 3X+2  0  X 2X 2X+2 X+2 X+2  X 3X+2 3X X+2  0 3X+2 3X 2X  0  2 2X+2  0 2X+2  X 2X  X X+2  2 2X  2 3X 3X  2 3X+2 3X  0 X+2 3X 2X 2X  X 3X+2 2X+2  X 2X 2X+2 X+2  X 3X 2X 3X 2X+2  2 3X  0 2X+2  X  X 2X 3X+2 2X+2  X  0 3X+2  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+140x^76+832x^77+1403x^78+2482x^79+3019x^80+3448x^81+3409x^82+4054x^83+3530x^84+3362x^85+2541x^86+1858x^87+1005x^88+800x^89+433x^90+210x^91+100x^92+74x^93+17x^94+12x^95+13x^96+12x^97+4x^98+8x^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 seconds.