The generator matrix

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

generates a code of length 73 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+135x^68+674x^69+930x^70+1118x^71+1110x^72+1032x^73+860x^74+672x^75+592x^76+494x^77+244x^78+150x^79+56x^80+68x^81+28x^82+12x^83+8x^84+4x^85+2x^86+1x^88+1x^92

The gray image is a code over GF(2) with n=584, k=13 and d=272.
This code was found by Heurico 1.16 in 0.89 seconds.