The generator matrix

 1  0  0  0  0  1  1  1  0 X^2  1  1 X^2  1  1  0  1 X^2+X  0  X  X  1  1  1  1  1 X^2+X  0  1  1  X X^2+X  1  1  X X^2 X^2  1 X^2  1  1  X  X X^2+X  1  1 X^2+X  X  1  0  1  1  X X^2+X  0  1  1  1  1  1  1  1
 0  1  0  0  0  0  0  0 X^2  0  0 X^2  0  0 X^2  X X^2+1  1  1  1  1 X^2+X+1 X^2+1  1 X+1 X^2+X+1 X^2+X  X  1 X^2+1  1  1 X^2+X+1 X^2+X  0  1  1 X^2  X X^2+X  0  X  X  1 X^2  X X^2+X  1 X^2+1  1 X+1 X^2+1 X^2 X^2+X  1 X^2+X+1  0  X X^2+X  1 X^2+1 X^2
 0  0  1  0  0  0  1  1  1  1 X^2+X X+1  X  X X^2+X+1  1 X^2+X+1  X  1 X^2+X+1 X^2+X+1  X X^2 X^2  0 X+1  0  1 X+1 X^2+X+1  0  0  1 X^2+X  1  1 X^2 X^2+1 X^2  1 X^2+X  1  1  1  0 X^2+1  1 X^2+1  0 X^2  X  1  1 X^2+X  1 X^2+X  0 X^2+X+1 X^2+X  1 X^2  X
 0  0  0  1  0  1  1 X^2 X^2+1 X^2+1  0  1  1 X+1  X X^2+X X^2+1  X  0 X^2+1 X^2+1 X^2+X X+1 X+1 X^2 X^2+X  0  X X^2+X+1 X^2+X X+1  1  X X^2+X X^2+1 X^2+X  X X^2+X+1  1 X+1 X^2+X+1 X+1 X^2 X^2 X^2+X X^2  0 X^2+X+1  X  0 X^2+1 X+1 X^2+1  1 X^2+1 X^2+1 X+1  1 X^2  0 X^2+1 X^2+X
 0  0  0  0  1  1 X^2 X^2+1  1  X X+1 X^2+X+1 X^2+X+1  0  0 X^2+X+1  1 X^2+X+1 X^2+X X^2 X^2+X+1 X+1 X^2 X^2+1  X X^2+X  1  1 X^2+X X^2+1  0 X+1  0 X^2+X X^2+X X+1  0 X^2+X X+1 X^2+X+1 X^2+X+1 X^2+1  1  X  1  0 X^2+X  0  X X^2+X  X X+1 X+1 X^2+X+1  0 X^2+X+1 X^2+X+1 X^2+X+1 X+1 X^2+X X+1 X^2+X
 0  0  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0  0  0 X^2  0 X^2

generates a code of length 62 over Z2[X]/(X^3) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+143x^52+554x^53+1013x^54+1626x^55+2175x^56+3134x^57+4481x^58+4598x^59+5720x^60+5680x^61+6662x^62+6296x^63+5970x^64+4844x^65+4387x^66+3040x^67+2094x^68+1374x^69+820x^70+438x^71+270x^72+110x^73+44x^74+26x^75+11x^76+16x^77+1x^78+8x^79

The gray image is a linear code over GF(2) with n=248, k=16 and d=104.
This code was found by Heurico 1.13 in 48.3 seconds.