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

generates a code of length 60 over Z2[X]/(X^3) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+141x^52+8x^53+312x^54+64x^55+403x^56+168x^57+506x^58+272x^59+488x^60+280x^61+496x^62+160x^63+267x^64+56x^65+220x^66+16x^67+125x^68+56x^70+40x^72+10x^74+6x^76+1x^88

The gray image is a linear code over GF(2) with n=240, k=12 and d=104.
This code was found by Heurico 1.16 in 1.2 seconds.