The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+788x^53+2181x^54+3828x^55+5863x^56+6906x^57+8613x^58+9358x^59+8831x^60+7040x^61+5688x^62+3366x^63+1793x^64+794x^65+249x^66+122x^67+55x^68+40x^69+5x^70+14x^71+1x^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 32.3 seconds.