The generator matrix

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

generates a code of length 84 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+81x^78+978x^79+1172x^80+1732x^81+1718x^82+2154x^83+1662x^84+2106x^85+1133x^86+1356x^87+813x^88+692x^89+300x^90+226x^91+128x^92+66x^93+24x^94+18x^95+5x^96+10x^97+4x^99+2x^100+1x^104+2x^105

The gray image is a code over GF(2) with n=672, k=14 and d=312.
This code was found by Heurico 1.16 in 4.06 seconds.