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

generates a code of length 84 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+550x^77+1726x^78+3058x^79+4588x^80+5510x^81+6753x^82+7222x^83+7769x^84+7168x^85+6785x^86+4706x^87+4013x^88+2684x^89+1451x^90+922x^91+307x^92+142x^93+109x^94+28x^95+26x^96+6x^97+8x^98+4x^101

The gray image is a code over GF(2) with n=672, k=16 and d=308.
This code was found by Heurico 1.16 in 46.5 seconds.