The generator matrix

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

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+34x^45+41x^46+84x^47+97x^48+112x^49+158x^50+178x^51+232x^52+212x^53+235x^54+176x^55+148x^56+128x^57+58x^58+60x^59+22x^60+26x^61+11x^62+12x^63+8x^64+6x^66+2x^67+1x^68+1x^70+2x^72+2x^74+1x^84

The gray image is a linear code over GF(2) with n=212, k=11 and d=90.
This code was found by Heurico 1.16 in 16.4 seconds.