The generator matrix

 1  0  1  1  1 X^2+X  1  1  0  1  1 X^2+X  1 X^2+X  1  1  0  1  1  0  1  1  1 X^2+X  1  0  1  1  1 X^2+X  1 X^2+X  1  1  0  0 X^2+X  1  1  1 X^2+X  1  1  1  0  1  1  1  1 X^2+X  1  1  X  1  1  1  1  1  1  1  1  1
 0  1 X+1 X^2+X  1  1  0 X+1  1 X^2+X X^2+1  1 X^2+X  1 X+1  0  1 X^2+1  0  1 X+1 X^2+X X^2+1  1  0  1 X+1 X^2+1 X^2+X  1 X^2+1  1 X^2+X X^2+1  1  1  1 X+1  0 X+1  1 X^2+1 X^2 X^2+X  1 X+1 X+1  0 X^2+1  1 X^2+X+1  0  1 X+1 X^2+X  0 X^2  X X^2+1 X+1 X+1  0
 0  0 X^2  0  0  0  0  0  0  0  0  0  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2
 0  0  0 X^2  0  0  0  0  0  0  0  0 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0  0  0  0 X^2 X^2 X^2  0  0 X^2  0 X^2  0  0 X^2  0 X^2  0 X^2  0 X^2  0  0  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  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  0 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0 X^2  0 X^2
 0  0  0  0  0 X^2  0  0  0  0  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0  0  0  0  0 X^2  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0  0  0  0
 0  0  0  0  0  0 X^2  0  0  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0  0  0  0 X^2  0
 0  0  0  0  0  0  0 X^2  0  0  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2  0 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2  0
 0  0  0  0  0  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0  0 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0  0
 0  0  0  0  0  0  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0  0  0 X^2  0 X^2  0 X^2  0  0 X^2  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+42x^50+22x^51+101x^52+78x^53+211x^54+262x^55+550x^56+558x^57+1149x^58+892x^59+1926x^60+1260x^61+2349x^62+1260x^63+1913x^64+892x^65+1133x^66+558x^67+523x^68+262x^69+175x^70+78x^71+71x^72+22x^73+39x^74+24x^76+15x^78+8x^80+5x^82+2x^84+2x^86+1x^88

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 14.1 seconds.