The generator matrix

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

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+155x^52+566x^53+785x^54+1250x^55+1551x^56+2286x^57+2286x^58+2902x^59+2952x^60+3406x^61+2812x^62+3066x^63+2441x^64+2178x^65+1472x^66+1190x^67+657x^68+384x^69+183x^70+132x^71+43x^72+40x^73+14x^74+4x^75+8x^76+4x^77

The gray image is a linear code over GF(2) with n=244, k=15 and d=104.
This code was found by Heurico 1.16 in 39.4 seconds.