The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2+2  1  1 X+2  1  1  0  1  1 X^2+X  1  1 X^2+2  1  1 X+2  1  1  0  1  1 X^2+X  1  1 X+2  1  1 X^2+2  1  2  1  1  1  1 X^2+X X^2  1 X+2  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0 X^2+X+2 X^2+2  X  0 X^2+2 X^2+X  1  1  1  1  1  2  1
 0  1 X+1 X^2+X X^2+1  1 X^2+X+3 X^2+2  1 X+2  3  1  0 X+1  1 X^2+X X^2+1  1 X^2+2 X^2+X+3  1 X+2  3  1  0 X+1  1 X^2+X X^2+1  1 X+2 X^2+X+3  1  3 X^2+2  1  2  1 X+1 X^2+X X^2 X^2+1  1  1 X+2  1 X^2+X+3  3 X^2+X+2  0  X X^2+2  0 X^2+X X^2+2 X^2+X X+2  0  2 X^2+X+2 X^2+2 X+2 X^2  X  1  1  1  1  1  1  1 X+3 X^2+X+1 X^2+3  1 X+1  1 X+3
 0  0  2  0  0  0  0  2  2  2  2  2  0  0  0  2  2  2  2  2  2  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  0  0  0  2  2  0  0  2  0  2  2  2  2  2  0  0  2  2  0  0  0  2  2  0  0  2  0  2  2  2  0  0  2  0  0  2  2  2  0  2  2  2
 0  0  0  2  0  2  2  2  2  0  2  0  0  0  2  0  0  2  2  2  0  2  2  0  2  0  0  0  2  2  2  0  2  2  0  0  2  2  2  2  0  0  0  2  0  0  2  0  0  2  2  0  0  2  0  2  0  2  0  0  2  2  2  0  2  0  0  2  2  2  0  0  0  2  2  2  2  0
 0  0  0  0  2  0  2  2  2  2  0  2  2  0  2  0  2  0  0  2  0  2  0  2  2  2  2  2  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0  0  0  0  0  2  0  0  0  0  2  2  2  2  2  2  0  2  0  0  0  0  0  0  0  2  2  2  2  0  2  2  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+194x^74+224x^75+118x^76+224x^77+524x^78+224x^79+118x^80+224x^81+194x^82+1x^92+1x^108+1x^112

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 0.359 seconds.