The generator matrix

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

generates a code of length 62 over Z2[X]/(X^3) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+124x^56+286x^57+453x^58+330x^59+497x^60+352x^61+424x^62+300x^63+294x^64+226x^65+207x^66+190x^67+196x^68+84x^69+58x^70+8x^71+23x^72+12x^73+26x^74+4x^75+1x^76

The gray image is a linear code over GF(2) with n=248, k=12 and d=112.
This code was found by Heurico 1.11 in 0.265 seconds.