The generator matrix

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

generates a code of length 78 over Z4[X]/(X^3+2,2X) 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.