The generator matrix

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

generates a code of length 63 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+164x^53+587x^54+980x^55+1878x^56+2048x^57+3593x^58+3548x^59+5275x^60+4730x^61+6832x^62+5530x^63+7286x^64+5054x^65+5696x^66+3652x^67+3604x^68+1876x^69+1375x^70+824x^71+560x^72+194x^73+149x^74+56x^75+15x^76+12x^77+6x^78+2x^79+3x^80+2x^82+2x^84+2x^85

The gray image is a code over GF(2) with n=252, k=16 and d=106.
This code was found by Heurico 1.13 in 57.8 seconds.