The generator matrix

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

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+103x^44+284x^45+757x^46+1040x^47+1689x^48+1908x^49+2633x^50+2820x^51+3440x^52+3120x^53+3711x^54+3212x^55+2676x^56+1730x^57+1546x^58+896x^59+609x^60+242x^61+179x^62+92x^63+58x^64+10x^65+5x^66+4x^67+2x^69+1x^70

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 32.3 seconds.