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

generates a code of length 60 over Z2[X]/(X^3) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+41x^54+52x^55+81x^56+82x^57+60x^58+130x^59+161x^60+132x^61+59x^62+66x^63+64x^64+36x^65+27x^66+6x^67+7x^68+4x^69+4x^70+2x^71+6x^72+2x^73+1x^106

The gray image is a linear code over GF(2) with n=240, k=10 and d=108.
This code was found by Heurico 1.16 in 0.184 seconds.