The generator matrix

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

generates a code of length 62 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+109x^52+8x^53+369x^54+140x^55+950x^56+336x^57+1525x^58+620x^59+2007x^60+956x^61+2495x^62+916x^63+1966x^64+636x^65+1605x^66+356x^67+669x^68+108x^69+341x^70+16x^71+150x^72+4x^73+61x^74+31x^76+3x^78+5x^80+1x^82

The gray image is a code over GF(2) with n=248, k=14 and d=104.
This code was found by Heurico 1.16 in 13.7 seconds.