The generator matrix

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

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+167x^56+244x^57+348x^58+480x^59+440x^60+384x^61+348x^62+392x^63+274x^64+216x^65+216x^66+192x^67+139x^68+112x^69+68x^70+24x^71+24x^72+4x^73+12x^74+9x^76+2x^80

The gray image is a linear code over GF(2) with n=248, k=12 and d=112.
This code was found by Heurico 1.16 in 0.823 seconds.