The generator matrix

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

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+114x^75+888x^76+1450x^77+2149x^78+2776x^79+3655x^80+3776x^81+4167x^82+3380x^83+3432x^84+2472x^85+1846x^86+1250x^87+694x^88+292x^89+200x^90+70x^91+80x^92+22x^93+33x^94+10x^95+2x^96+4x^97+5x^98

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 14.3 seconds.