The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+448x^75+1866x^76+3096x^77+4120x^78+5754x^79+6389x^80+7510x^81+8106x^82+7218x^83+6406x^84+5372x^85+3965x^86+2520x^87+1322x^88+770x^89+388x^90+134x^91+52x^92+60x^93+21x^94+6x^95+4x^96+8x^97

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 47.4 seconds.