The generator matrix

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

generates a code of length 59 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+884x^53+2032x^54+3888x^55+5510x^56+7352x^57+8698x^58+9064x^59+8904x^60+7588x^61+5040x^62+3484x^63+1617x^64+888x^65+386x^66+104x^67+60x^68+24x^69+4x^70+4x^71+4x^72

The gray image is a code over GF(2) with n=472, k=16 and d=212.
This code was found by Heurico 1.16 in 180 seconds.