The generator matrix

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

generates a code of length 76 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+330x^69+1584x^70+2752x^71+4356x^72+5570x^73+6703x^74+7410x^75+8564x^76+7710x^77+6811x^78+5184x^79+3631x^80+2360x^81+1547x^82+546x^83+246x^84+116x^85+69x^86+12x^87+12x^88+10x^89+6x^90+6x^92

The gray image is a code over GF(2) with n=608, k=16 and d=276.
This code was found by Heurico 1.16 in 45.3 seconds.