The generator matrix

 1  0  1  1  1  0  1  1  0  1  2  1  1  1 X+2  1  X  1  1  X  X  1  1  1  1  2  2  1  1  X  2  1  1  2  1  1 X+2  1  1  1  0  1  1  1  X  1 X+2  1  1  X  1  1  1  1  X  1  1  1  0  X  1  X  1
 0  1  1  0  1  1  2 X+1  1  0  1  3 X+3  0  1  1  1  2  2  1  1 X+1  2  3  3  1  1  0 X+2  1  1 X+1  0  1 X+1  2  1 X+1 X+2 X+1  1 X+2  2  3  1  1  1  1  2  1  X  1  X  2  1 X+2 X+2 X+3  1  0  X X+2 X+2
 0  0  X  0  0  0  0  0  0  0  0  0  2  X X+2 X+2 X+2 X+2 X+2  X  X X+2  X  X  2  2  2  X  0  2 X+2  X  0  X  2 X+2  2  2  2  X  X X+2  0  X X+2  0  X  2 X+2 X+2  0  2  2  X  2  2  X  X  2  2 X+2 X+2  2
 0  0  0  X  0  0  0  0  X X+2 X+2  X X+2 X+2 X+2 X+2  0 X+2  2 X+2  2 X+2  0  0  2  X  0  0  2  2  X  0 X+2  2 X+2  X X+2  0  2  X  2  2 X+2  X  X  X  2  X  2 X+2  0  0  X  X  2  0  X X+2  2  0  0  X  X
 0  0  0  0  X  0  2 X+2  0  2  0 X+2  X  X  X  2  X X+2  X  X  X  0 X+2  2  0 X+2  X  2  X X+2  2  X  X  X  X  0  X  0 X+2  X  0 X+2 X+2  0  2  2  0  X  2  0  X X+2 X+2 X+2  2  2  2 X+2  X  2  X  X X+2
 0  0  0  0  0  X X+2 X+2 X+2 X+2  2  2  X X+2 X+2  2  2  0 X+2  0  X X+2  0 X+2  2  X  X  X X+2  0  2  X X+2  X  2 X+2  0 X+2  2  X X+2 X+2  X X+2 X+2  2  0 X+2  0  X  X  0  X  2  2 X+2  2  0  2 X+2  X  X  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+54x^53+127x^54+238x^55+438x^56+590x^57+734x^58+978x^59+1241x^60+1386x^61+1602x^62+1724x^63+1547x^64+1424x^65+1255x^66+996x^67+734x^68+474x^69+310x^70+202x^71+114x^72+90x^73+58x^74+18x^75+17x^76+14x^77+8x^78+4x^79+4x^80+1x^82+1x^86

The gray image is a code over GF(2) with n=252, k=14 and d=106.
This code was found by Heurico 1.16 in 13.8 seconds.