The generator matrix

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

generates a code of length 61 over Z2[X]/(X^3) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+96x^51+538x^52+1018x^53+1603x^54+2326x^55+3048x^56+4206x^57+4542x^58+5894x^59+5967x^60+6732x^61+6141x^62+6010x^63+4919x^64+4260x^65+3100x^66+2110x^67+1380x^68+802x^69+387x^70+288x^71+74x^72+30x^73+34x^74+12x^75+7x^76+8x^77+1x^78+2x^80

The gray image is a linear code over GF(2) with n=244, k=16 and d=102.
This code was found by Heurico 1.13 in 47.4 seconds.