The generator matrix

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

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+444x^74+408x^75+690x^76+344x^77+536x^78+440x^79+424x^80+296x^81+328x^82+48x^83+78x^84+24x^86+20x^88+12x^90+1x^96+2x^104

The gray image is a code over GF(2) with n=624, k=12 and d=296.
This code was found by Heurico 1.16 in 1.09 seconds.