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

generates a code of length 53 over Z2[X]/(X^3) who�s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+169x^44+405x^46+52x^47+624x^48+232x^49+806x^50+452x^51+1070x^52+600x^53+1118x^54+444x^55+884x^56+184x^57+506x^58+76x^59+314x^60+8x^61+147x^62+67x^64+24x^66+6x^68+2x^70+1x^76

The gray image is a linear code over GF(2) with n=212, k=13 and d=88.
This code was found by Heurico 1.16 in 4.33 seconds.