The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+660x^78+128x^79+789x^80+144x^81+890x^82+112x^83+669x^84+112x^85+368x^86+16x^87+137x^88+50x^90+1x^92+16x^94+1x^96+1x^100+1x^116

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 55.6 seconds.