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

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+139x^44+8x^45+418x^46+28x^47+600x^48+224x^49+866x^50+500x^51+1046x^52+552x^53+1190x^54+452x^55+806x^56+240x^57+506x^58+44x^59+339x^60+136x^62+72x^64+20x^66+4x^68+1x^80

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 4.12 seconds.