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

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+77x^76+152x^77+326x^78+240x^79+547x^80+484x^81+601x^82+436x^83+536x^84+188x^85+212x^86+128x^87+73x^88+12x^89+37x^90+12x^91+12x^92+12x^93+8x^94+1x^96+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 0.937 seconds.