The generator matrix

 1  0  0  1  1  1 X^2+X  1 X^2  1  X  1  1 X^2  1  1  X  1  0  1 X^2  X X^2  1  1 X^2  1  1  X  1  1  1  1  1  0  1 X^2+X X^2 X^2 X^2+X  1  X  1 X^2+X  1  X  1  X  1  1  1  1  1  1  1  X  1  1  X  1  1
 0  1  0  0  1  1  1  X  1  X  1 X+1  1  X X+1 X+1  0 X^2+X  1  0  1 X^2+X  1  1 X^2+X+1  1  0  X X^2+X X+1 X^2+X X^2+X+1 X^2 X^2  1 X^2+X+1  1  1 X^2+X  0 X^2+X+1  1 X+1  1 X^2+1  0 X+1 X^2+X X^2+X+1 X^2+X X^2+X+1 X^2+1 X^2+X+1 X^2 X^2+X  1 X+1 X+1  1 X^2  X
 0  0  1  1  1  0  1 X+1  X  X X^2+1  X  1  1 X+1  0  1 X^2+1 X^2+1 X^2+X  0  1 X^2 X^2  1 X^2+X+1 X+1 X^2  1 X^2+X X^2+X+1 X^2+1  X  X  1  1 X+1 X^2+X  1  1 X^2+X X^2+X  X X^2  1  1 X+1  1  1 X+1  0 X^2+X+1 X^2 X^2 X^2+1 X^2 X^2 X+1  0  X  X
 0  0  0  X  0  0  0  0  X X^2+X X^2+X X^2+X X^2  X X^2+X X^2+X  X  X  0  0 X^2 X^2  X  0 X^2+X X^2+X  0 X^2+X X^2+X  0  X X^2+X X^2 X^2+X X^2 X^2 X^2+X X^2+X X^2+X  0 X^2 X^2 X^2  X X^2+X  0  X  0  0  0 X^2  X X^2 X^2+X X^2+X  0 X^2 X^2  X  0  X
 0  0  0  0  X  0  0  0  0  0  0  0  0 X^2 X^2  X  X X^2+X X^2+X  X X^2+X  X  X  X X^2+X X^2+X  X  X X^2 X^2  X X^2  0  X X^2+X  0 X^2 X^2 X^2+X X^2 X^2+X X^2 X^2  X X^2+X  X X^2+X X^2  0 X^2+X X^2+X  0 X^2 X^2+X  X  0 X^2  X  0  X  X
 0  0  0  0  0  X X^2+X X^2+X X^2+X  X  0 X^2  0  X  X  0  X  0 X^2+X X^2  0  0 X^2+X  X  X  0  X X^2+X  X X^2 X^2+X X^2  X  0 X^2  X  X X^2 X^2  X  0 X^2+X  0 X^2  X X^2+X  0  X X^2 X^2 X^2+X  0  X X^2  X  X X^2 X^2+X X^2 X^2+X  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+70x^51+266x^52+508x^53+714x^54+1136x^55+1561x^56+1908x^57+2405x^58+2928x^59+3246x^60+3386x^61+3255x^62+2828x^63+2474x^64+2016x^65+1523x^66+1002x^67+639x^68+408x^69+209x^70+148x^71+64x^72+28x^73+20x^74+16x^75+5x^76+2x^77+2x^78

The gray image is a linear code over GF(2) with n=244, k=15 and d=102.
This code was found by Heurico 1.16 in 41.4 seconds.