The generator matrix

 1  0  0  0  0  1  1  1  0 X^2  1  1  1  0  0  1  1 X^2+X  1  0  1  1  0  X  1  X  1 X^2  1 X^2+X X^2+X  1  1  1  0  1  1 X^2+X  1  1 X^2 X^2  1 X^2+X  0  X  1  X X^2+X  1  1 X^2+X  0
 0  1  0  0  0  0  0  0 X^2  0  0 X^2  0  0 X^2  X  1  1 X+1  1  1 X+1  1  1 X+1  1 X^2+X  1 X^2+1  1 X^2 X+1 X^2+1 X^2+X+1 X^2+X  X  X  1 X^2  X  X X^2  1  1  1  1 X+1 X^2+X  0  X X^2+1  1  1
 0  0  1  0  0  0  1  1  1  1 X^2 X^2+X+1 X+1  1  X  X X^2+X  X X^2+X X^2+X+1  0 X^2+X+1  1 X^2 X^2+X+1 X^2+X+1  0  X X+1 X+1  X X^2+X+1  1 X+1  1 X^2+1  1  1 X^2+X+1 X+1 X^2  1  0 X^2+1  1 X^2+X X^2+X  1 X^2+X X^2 X+1  1  X
 0  0  0  1  0  1  1 X^2 X^2+1 X^2+1  X  1  X X^2+X  1 X+1 X^2  0 X+1 X^2 X+1  1 X^2+X+1 X^2+X+1  0 X^2+X X^2+X X+1  X X^2+X+1  1 X^2+X+1  X X+1  1 X^2+X  1  0 X^2 X^2+X+1 X^2+X  X  0 X+1  X X^2+1 X^2  0  X X^2+X+1 X^2+1 X^2+X+1  0
 0  0  0  0  1  1 X^2 X^2+1 X^2+1  X X^2+X+1 X^2+X+1  0 X+1 X+1 X^2 X+1 X^2+1 X^2+X  1 X^2+X+1 X^2  1  X X+1 X^2 X^2+X X+1  0  0  X X+1 X^2+1 X^2  1  0  1  X X^2+X X^2  1  1  X  0 X+1  0  X  0  1  1  X X+1 X+1
 0  0  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2  0  0  0 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2 X^2  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+264x^44+824x^45+1460x^46+1848x^47+3203x^48+3736x^49+5438x^50+5696x^51+6898x^52+6288x^53+7344x^54+5896x^55+5516x^56+4020x^57+3012x^58+1732x^59+1290x^60+544x^61+252x^62+120x^63+96x^64+12x^65+30x^66+4x^67+12x^68

The gray image is a linear code over GF(2) with n=212, k=16 and d=88.
This code was found by Heurico 1.13 in 40 seconds.