The generator matrix

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

generates a code of length 76 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+36x^71+120x^72+312x^73+184x^74+320x^75+340x^76+144x^77+228x^78+36x^79+115x^80+152x^81+35x^82+24x^83+1x^130

The gray image is a code over GF(2) with n=608, k=11 and d=284.
This code was found by Heurico 1.16 in 2.06 seconds.