The generator matrix

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

generates a code of length 78 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+94x^74+344x^75+220x^76+348x^77+195x^78+270x^79+117x^80+244x^81+125x^82+72x^83+11x^84+2x^87+2x^88+1x^100+1x^102+1x^106

The gray image is a code over GF(2) with n=624, k=11 and d=296.
This code was found by Heurico 1.16 in 0.547 seconds.