The generator matrix

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

generates a code of length 59 over Z2[X]/(X^3) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+106x^54+220x^55+267x^56+266x^57+208x^58+206x^59+166x^60+140x^61+108x^62+88x^63+86x^64+58x^65+47x^66+22x^67+24x^68+16x^69+8x^70+8x^71+3x^74

The gray image is a linear code over GF(2) with n=236, k=11 and d=108.
This code was found by Heurico 1.16 in 0.232 seconds.