The generator matrix

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

generates a code of length 82 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+476x^75+1858x^76+2888x^77+4385x^78+5582x^79+6809x^80+7364x^81+7724x^82+7220x^83+6692x^84+5106x^85+4248x^86+2390x^87+1410x^88+736x^89+308x^90+200x^91+74x^92+34x^93+19x^94+4x^96+4x^98+4x^99

The gray image is a code over GF(2) with n=656, k=16 and d=300.
This code was found by Heurico 1.16 in 49.6 seconds.