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  1  1  1  X X^2  X X^2  X  X  X  0  1  X  X  1  0  1 X^2  1  1 X^2  X  1  X X^2  1  1  1
 0  X  0  0  0  0  0  0  0 X^2+X  X  X  X  X X^2 X^2  0  X X^2 X^2+X  X  0 X^2 X^2  X  0  X X^2+X X^2 X^2+X  0  X X^2+X X^2+X X^2 X^2  X X^2  X  X X^2+X X^2 X^2+X  X  X  0 X^2+X  X X^2 X^2 X^2 X^2+X  0  X X^2+X X^2  0  X  X X^2  0
 0  0  X  0  0  0  X X^2+X  X X^2  X X^2+X  0  0  X X^2+X X^2+X X^2+X  0 X^2  X X^2+X X^2+X X^2+X  X X^2 X^2+X  X X^2+X  0  0 X^2  X X^2+X  0 X^2 X^2+X  X X^2  0 X^2  X  0  0  X X^2 X^2+X  0  0 X^2+X  X  X  X  X X^2+X  X X^2 X^2+X  X  0  X
 0  0  0  X  0  X  X  X  0 X^2+X X^2  X X^2+X  0  X X^2+X  0  0 X^2+X  X X^2  X X^2  0 X^2  0  X  X  0  X  0  0 X^2 X^2+X X^2 X^2+X X^2+X  0  0 X^2  0 X^2  0 X^2  X  X  X X^2  X  X  0  X X^2+X X^2+X X^2+X X^2 X^2  0  X  X  0
 0  0  0  0  X  X  0  X X^2+X  X  0  X X^2 X^2+X X^2+X  0  X X^2+X X^2 X^2  0 X^2+X  0  X  0  X X^2+X  0 X^2 X^2+X X^2 X^2  X X^2+X  0 X^2+X X^2+X  X X^2+X  X X^2 X^2 X^2 X^2  0  X X^2+X X^2+X X^2  X  0 X^2+X  0 X^2+X X^2 X^2+X  X X^2 X^2  X  X
 0  0  0  0  0 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0 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 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0  0  0  0  0 X^2  0  0  0  0 X^2  0 X^2 X^2  0 X^2  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+44x^51+120x^52+160x^53+246x^54+236x^55+502x^56+226x^57+974x^58+258x^59+1253x^60+264x^61+1260x^62+244x^63+966x^64+208x^65+486x^66+160x^67+172x^68+144x^69+78x^70+72x^71+50x^72+22x^73+27x^74+10x^75+7x^76+1x^80+1x^90

The gray image is a linear code over GF(2) with n=244, k=13 and d=102.
This code was found by Heurico 1.16 in 5.21 seconds.