The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  2  X  2  X  X  X  0  1  X  X  1  0  1  2  1  1  2  1  X  1  2  1  0  1  1  1
 0  X  0  0  0  0  0  0  0 X+2  X  X  X  X  2  2  0  X  2 X+2  X  0  2  2  X  0  X X+2  2 X+2  0  X X+2 X+2  2  2  X  2  X  X X+2  2 X+2  X  X  0 X+2  X  2  2  2  0 X+2  X  X X+2 X+2  X  2  X  X  X  X
 0  0  X  0  0  0  X X+2  X  2  X X+2  0  0  X X+2 X+2 X+2  0  2  X X+2 X+2 X+2  X  2 X+2  X X+2  0  0  2  X X+2  0  2 X+2  X  2  0  2  X  0  0  X  2 X+2  0  0 X+2  X  X X+2  0  2  2  2 X+2  0  X  2  X  X
 0  0  0  X  0  X  X  X  0 X+2  2  X X+2  0  X X+2  0  0 X+2  X  2  X  2  0  2  0  X  X  0  X  0  0  2 X+2  2 X+2 X+2  0  0  2  0  2  0  2  X  X  X  2  X  X  0  2  X  0  X  0  2  X X+2  0  2  X  2
 0  0  0  0  X  X  0  X X+2  X  0  X  2 X+2 X+2  0  X X+2  2  2  0 X+2  0  X  0  X X+2  0  2 X+2  2  2  X X+2  0 X+2 X+2  X X+2  X  2  2  2  2  0  X X+2 X+2  2  X  0  0  0  X  2 X+2 X+2 X+2  X  X  2  X  2
 0  0  0  0  0  2  0  0  0  0  0  0  0  2  2  2  2  2  2  0  2  0  2  0  2  2  2  0  0  2  2  2  0  2  2  2  2  0  0  2  0  2  2  2  2  2  0  0  2  2  2  2  0  2  2  0  0  2  0  0  2  2  0
 0  0  0  0  0  0  2  0  2  0  2  2  2  2  0  2  2  0  2  0  2  2  2  0  0  2  2  0  2  0  2  2  2  0  0  2  2  0  2  0  0  2  0  2  0  0  0  0  0  2  0  0  2  2  2  2  2  2  0  2  2  2  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+52x^53+109x^54+160x^55+266x^56+292x^57+370x^58+458x^59+591x^60+738x^61+720x^62+750x^63+765x^64+752x^65+620x^66+404x^67+309x^68+264x^69+170x^70+120x^71+81x^72+64x^73+53x^74+26x^75+32x^76+10x^77+4x^78+2x^79+3x^80+4x^81+1x^82+1x^94

The gray image is a code over GF(2) with n=252, k=13 and d=106.
This code was found by Heurico 1.16 in 5.5 seconds.