The generator matrix

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

generates a code of length 61 over Z2[X]/(X^3) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+122x^52+500x^53+866x^54+1360x^55+1654x^56+2032x^57+2393x^58+2874x^59+2961x^60+3248x^61+2933x^62+3124x^63+2349x^64+2114x^65+1582x^66+1100x^67+763x^68+412x^69+181x^70+92x^71+54x^72+26x^73+11x^74+10x^75+4x^77+2x^78

The gray image is a linear code over GF(2) with n=244, k=15 and d=104.
This code was found by Heurico 1.13 in 12.4 seconds.