The generator matrix

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

generates a code of length 62 over Z2[X]/(X^3) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+53x^50+72x^51+165x^52+216x^53+325x^54+450x^55+467x^56+746x^57+873x^58+1104x^59+1379x^60+1498x^61+1659x^62+1538x^63+1438x^64+1152x^65+896x^66+716x^67+441x^68+408x^69+220x^70+170x^71+157x^72+70x^73+65x^74+44x^75+45x^76+6x^77+3x^78+2x^79+1x^80+1x^82+2x^84+1x^86

The gray image is a linear code over GF(2) with n=248, k=14 and d=100.
This code was found by Heurico 1.16 in 19.5 seconds.