The generator matrix

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

generates a code of length 62 over Z2[X]/(X^3) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+238x^58+187x^60+212x^62+150x^64+208x^66+12x^68+12x^70+2x^74+1x^92+1x^96

The gray image is a linear code over GF(2) with n=248, k=10 and d=116.
This code was found by Heurico 1.16 in 1.3 seconds.