The generator matrix

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

generates a code of length 62 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+124x^53+538x^54+896x^55+1180x^56+1730x^57+2252x^58+2334x^59+2815x^60+2890x^61+3311x^62+2880x^63+3076x^64+2492x^65+2042x^66+1424x^67+1064x^68+810x^69+451x^70+224x^71+117x^72+62x^73+44x^74+2x^75+3x^76+4x^77+2x^78

The gray image is a code over GF(2) with n=248, k=15 and d=106.
This code was found by Heurico 1.13 in 14.8 seconds.