The generator matrix

 1  0  0  0  1  1  1  0  1  X  X X^2+X  1  1  1  1  1  1  1  1  1  1  X X^2  X X^2  1  X X^2  1 X^2  1 X^2  0  0  1  1 X^2 X^2 X^2  1 X^2+X  1  1  0  1  1  1  1 X^2+X  1  X  1
 0  1  0  0  0  1  1  1 X^2 X^2+X  1  1 X^2 X^2+1 X^2+X+1 X^2  X X^2+1 X^2+X+1 X^2 X^2+X  1  1 X^2+X  X  1 X^2+1  0  X  1  1 X+1  1  1  1 X^2+1 X^2+X+1  1 X^2  1  X  X  X X^2+X+1  1  0  1 X^2  0  1  0  1  0
 0  0  1  0  1  1 X^2 X^2+1 X^2+X+1  1 X^2  1  X X^2+1  0 X^2+1 X^2 X+1 X^2+X X^2  1  X X^2+1  1 X^2  1 X^2+1  1 X^2 X+1  0  X X+1  X X^2+X  0 X^2+1  0  0 X^2+X+1 X^2+X  1 X+1 X^2+X  1  1  X X^2+1 X^2+X+1 X^2+1 X^2+1  1  0
 0  0  0  1  1  0 X^2+1  1 X^2  1 X+1  X X+1  1 X^2 X+1  1  0 X^2  0 X^2+X X^2+X+1 X+1  0  1  X  1 X^2+X+1  1 X^2+X+1 X^2 X^2+X X^2+X  1 X^2 X+1 X+1 X^2+X  1  1  X X+1 X^2  X  X X^2+X+1 X^2+X X^2+X X^2+1 X^2+X+1  X  X X^2+X
 0  0  0  0  X  0  0  0  0  0  0  0  0 X^2 X^2 X^2  X  X  X X^2+X  X  X X^2+X X^2+X  X X^2 X^2+X  X  0  0 X^2+X X^2  X X^2  X  0  X X^2  X  0  X X^2 X^2  X  X X^2+X X^2+X  X X^2+X X^2+X  X X^2  X
 0  0  0  0  0 X^2  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  0 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 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+89x^44+338x^45+757x^46+1072x^47+1527x^48+2038x^49+2426x^50+2920x^51+3395x^52+3552x^53+3373x^54+3166x^55+2603x^56+2008x^57+1441x^58+910x^59+518x^60+274x^61+190x^62+90x^63+53x^64+10x^65+5x^66+2x^67+6x^68+4x^69

The gray image is a linear code over GF(2) with n=212, k=15 and d=88.
This code was found by Heurico 1.16 in 31.1 seconds.