The generator matrix

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

generates a code of length 82 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+230x^76+28x^77+252x^78+144x^79+493x^80+588x^81+746x^82+608x^83+437x^84+148x^85+154x^86+16x^87+132x^88+4x^89+62x^90+31x^92+2x^94+14x^96+5x^100+1x^140

The gray image is a code over GF(2) with n=656, k=12 and d=304.
This code was found by Heurico 1.16 in 5.13 seconds.