The generator matrix

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

generates a code of length 62 over Z2[X]/(X^3) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+211x^54+366x^55+830x^56+808x^57+1260x^58+1126x^59+1545x^60+1342x^61+1601x^62+1270x^63+1659x^64+1172x^65+1019x^66+712x^67+748x^68+234x^69+250x^70+104x^71+74x^72+24x^73+9x^74+6x^75+7x^76+4x^77+2x^78

The gray image is a linear code over GF(2) with n=248, k=14 and d=108.
This code was found by Heurico 1.13 in 3.63 seconds.