The generator matrix

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

generates a code of length 53 over Z2[X]/(X^3) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+348x^45+698x^46+1260x^47+1603x^48+2126x^49+2388x^50+3086x^51+2921x^52+3672x^53+3150x^54+3232x^55+2501x^56+2244x^57+1418x^58+1070x^59+483x^60+294x^61+146x^62+56x^63+39x^64+18x^65+6x^66+4x^68+2x^69+2x^70

The gray image is a linear code over GF(2) with n=212, k=15 and d=90.
This code was found by Heurico 1.13 in 32.2 seconds.