The generator matrix

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

generates a code of length 73 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+140x^69+712x^70+560x^71+664x^72+494x^73+524x^74+256x^75+225x^76+166x^77+161x^78+68x^79+85x^80+12x^81+25x^82+1x^86+1x^88+1x^94

The gray image is a code over GF(2) with n=584, k=12 and d=276.
This code was found by Heurico 1.16 in 0.297 seconds.