The generator matrix

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

generates a code of length 74 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+148x^69+198x^70+512x^71+516x^72+440x^73+575x^74+482x^75+397x^76+440x^77+194x^78+114x^79+25x^80+28x^81+8x^82+4x^83+2x^84+6x^87+2x^88+2x^91+1x^106+1x^108

The gray image is a code over GF(2) with n=592, k=12 and d=276.
This code was found by Heurico 1.16 in 0.64 seconds.