The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+117x^76+764x^77+1133x^78+2006x^79+1632x^80+2172x^81+1788x^82+1960x^83+1382x^84+1214x^85+678x^86+778x^87+306x^88+228x^89+68x^90+64x^91+37x^92+22x^93+9x^94+8x^95+13x^96+4x^98

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 3.98 seconds.