The generator matrix

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

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+108x^71+650x^72+972x^73+1250x^74+1132x^75+1041x^76+670x^77+664x^78+596x^79+459x^80+228x^81+182x^82+116x^83+73x^84+14x^85+29x^86+4x^89+2x^90+1x^94

The gray image is a code over GF(2) with n=608, k=13 and d=284.
This code was found by Heurico 1.16 in 1.05 seconds.