The generator matrix

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

generates a code of length 63 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+212x^55+402x^56+848x^57+885x^58+1158x^59+1046x^60+1564x^61+1276x^62+1750x^63+1280x^64+1562x^65+1134x^66+1120x^67+685x^68+672x^69+319x^70+218x^71+99x^72+90x^73+33x^74+22x^75+5x^76+2x^80+1x^86

The gray image is a code over GF(2) with n=252, k=14 and d=110.
This code was found by Heurico 1.16 in 10.4 seconds.