The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+404x^73+173x^74+512x^75+129x^76+328x^77+113x^78+244x^79+25x^80+84x^81+16x^83+4x^84+4x^85+1x^86+4x^87+4x^89+1x^98+1x^108

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 225 seconds.