The generator matrix

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

generates a code of length 76 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+390x^73+343x^74+272x^75+227x^76+232x^77+175x^78+240x^79+75x^80+54x^81+8x^82+20x^83+4x^85+1x^86+4x^87+1x^100+1x^106

The gray image is a code over GF(2) with n=608, k=11 and d=292.
This code was found by Heurico 1.16 in 1.86 seconds.