The generator matrix

 1  0  0  1  1  1 2X+2 2X  0  2  1  1  1  1 X+2 X+2  1 X+2  1  1  1 X+2  1 3X+2  1  1  1 X+2 X+2  1  1 2X 2X  1  1  1  1  1  X  2  1  1  X 2X  1  1  1 3X+2 3X+2  1  1  1  2  2  1  1  1 2X  1  1  1  1  1  1 2X+2  X  1  1  1  1  2  1 3X+2  X 3X  1  1  1 X+2  1  2  1
 0  1  0  0  3 2X+3  1 X+2  1  1 2X+2  2 2X+3 2X+3 2X+2  1 X+1  1 3X+2  X 3X+3 3X 3X+2  1 3X 3X+1 X+3  1 2X+2 2X+2 2X+1  1  1  2 X+1 X+2 2X+1 3X+3  1  0  X 2X 3X+2  1 3X+1  3 X+2  1  1 2X+3 3X+1  0 3X+2  1 3X 3X+1 2X+1  1 2X+2 3X X+3 2X X+2  X  1 2X  0 X+2 X+2 3X  1  2 X+2  1  1 3X  1  X  1  3 X+2  0
 0  0  1 X+1 X+3  2 X+3  1 3X+2  1 3X  1  1 3X  1 3X+2 3X+2 2X+1 2X+1  X  1  1 3X+1 2X+2  2 X+3 2X+2 X+1  1 2X X+1  0 2X+1 X+1 3X+2 3X+3 2X+2  3  3  1  3 2X  1 3X+3 X+2 2X+3  0 X+3  0 X+2 X+3 X+2  1 X+2 X+2  3  0 2X+3 2X+3 3X 2X  X  1 X+1  1  1 X+1 X+3 2X+3 3X+2  0 3X+1  1 X+2 X+2  0 2X+2  1 2X+2  2  1  0
 0  0  0  2  2  0  2 2X+2  2 2X  2  0 2X 2X+2 2X+2  0  0  2  2  2  2 2X  0 2X+2 2X+2 2X 2X 2X  0 2X  0 2X+2  2 2X 2X+2 2X+2  2 2X+2  0  2  0 2X+2 2X+2 2X  2 2X+2 2X  0 2X  0 2X+2 2X  0  0 2X+2 2X  2  0 2X  0  2 2X+2  0 2X 2X+2 2X  0  2 2X+2 2X  0 2X+2 2X+2 2X+2 2X  0  0  2  2 2X 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+203x^76+850x^77+1046x^78+1676x^79+1654x^80+2480x^81+1719x^82+1936x^83+1305x^84+1258x^85+811x^86+696x^87+319x^88+192x^89+70x^90+102x^91+22x^92+20x^93+9x^94+4x^95+6x^96+1x^98+2x^99+2x^100

The gray image is a code over GF(2) with n=656, k=14 and d=304.
This code was found by Heurico 1.16 in 4.08 seconds.