The generator matrix

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

generates a code of length 79 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+118x^74+396x^75+435x^76+508x^77+360x^78+596x^79+388x^80+416x^81+356x^82+284x^83+99x^84+100x^85+24x^86+4x^87+3x^88+2x^94+2x^102+2x^106+2x^108

The gray image is a code over GF(2) with n=632, k=12 and d=296.
This code was found by Heurico 1.16 in 0.625 seconds.