The generator matrix

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

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+156x^75+816x^76+1642x^77+2211x^78+2920x^79+3417x^80+3834x^81+3801x^82+3708x^83+2840x^84+2612x^85+2036x^86+1208x^87+719x^88+410x^89+221x^90+112x^91+34x^92+30x^93+19x^94+8x^95+13x^96

The gray image is a code over GF(2) with n=656, k=15 and d=300.
This code was found by Heurico 1.16 in 13.4 seconds.