The generator matrix

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

generates a code of length 84 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+423x^76+1662x^77+3476x^78+6008x^79+7629x^80+10940x^81+12705x^82+15008x^83+15314x^84+15338x^85+13337x^86+11342x^87+6949x^88+5058x^89+2980x^90+1580x^91+751x^92+306x^93+137x^94+66x^95+35x^96+6x^97+5x^98+8x^99+2x^100+2x^101+4x^103

The gray image is a code over GF(2) with n=672, k=17 and d=304.
This code was found by Heurico 1.16 in 204 seconds.