The generator matrix

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

generates a code of length 62 over Z2[X]/(X^3) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+84x^57+214x^58+322x^59+263x^60+180x^61+220x^62+186x^63+127x^64+104x^65+85x^66+58x^67+68x^68+36x^69+19x^70+38x^71+20x^72+12x^73+5x^74+4x^75+1x^76+1x^78

The gray image is a linear code over GF(2) with n=248, k=11 and d=114.
This code was found by Heurico 1.16 in 0.252 seconds.