The generator matrix

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

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+282x^53+965x^54+1910x^55+3033x^56+4038x^57+3967x^58+4712x^59+4337x^60+3818x^61+2459x^62+1626x^63+828x^64+434x^65+241x^66+52x^67+23x^68+20x^69+16x^70+4x^71+2x^72

The gray image is a code over GF(2) with n=472, k=15 and d=212.
This code was found by Heurico 1.16 in 8.59 seconds.