The generator matrix

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

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+154x^55+141x^56+374x^57+263x^58+344x^59+244x^60+248x^61+81x^62+86x^63+24x^64+50x^65+6x^66+8x^67+6x^68+16x^69+1x^70+1x^90

The gray image is a code over GF(2) with n=472, k=11 and d=220.
This code was found by Heurico 1.16 in 0.218 seconds.