The generator matrix

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

generates a code of length 59 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+634x^55+739x^56+1362x^57+1048x^58+1432x^59+679x^60+908x^61+403x^62+486x^63+231x^64+194x^65+20x^66+32x^67+13x^68+8x^69+1x^70+1x^72

The gray image is a code over GF(2) with n=472, k=13 and d=220.
This code was found by Heurico 1.16 in 0.64 seconds.