The generator matrix

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

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+112x^69+708x^70+840x^71+1373x^72+932x^73+1074x^74+812x^75+732x^76+436x^77+548x^78+220x^79+233x^80+84x^81+54x^82+12x^83+1x^84+4x^85+8x^86+4x^87+3x^88+1x^92

The gray image is a code over GF(2) with n=592, k=13 and d=276.
This code was found by Heurico 1.16 in 0.89 seconds.