The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+454x^76+1806x^77+3413x^78+5644x^79+7632x^80+11200x^81+12561x^82+15108x^83+15445x^84+15404x^85+13215x^86+10970x^87+7564x^88+5156x^89+2598x^90+1582x^91+609x^92+358x^93+192x^94+66x^95+37x^96+28x^97+19x^98+6x^99+2x^100+2x^102

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 182 seconds.