The generator matrix

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

generates a code of length 82 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+200x^78+556x^79+734x^80+756x^81+496x^82+276x^83+250x^84+234x^85+164x^86+204x^87+109x^88+30x^89+49x^90+24x^91+9x^92+2x^94+1x^96+1x^102

The gray image is a code over GF(2) with n=656, k=12 and d=312.
This code was found by Heurico 1.16 in 0.406 seconds.