The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  1  1  X  0  0 X^2  1  X  X  1  1  1  0  1 X^2  0  1  1 X^2  1  1  0  1  0 X^2  X  1
 0  X  0  X  0  0  X X^2+X  0 X^2 X^2+X  X  0  X  X X^2 X^2 X^2+X  0  X X^2+X  0  X X^2 X^2+X  X  X  X  0 X^2  0  X  0 X^2+X X^2  0 X^2+X  X  0 X^2+X  X  X X^2+X  X  X  X  X  X X^2+X  X X^2  X  0
 0  0  X  X  0 X^2+X  X  0 X^2  X  0  X  0 X^2+X X^2  X  X X^2  0 X^2+X X^2+X  X X^2  0  0 X^2 X^2  X X^2+X  X  X  X  X  0  X  0  0 X^2+X  X  X X^2+X  X  X  X X^2+X X^2  X X^2 X^2  0  X  X  0
 0  0  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0 X^2 X^2  0
 0  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0  0  0  0
 0  0  0  0  0 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0  0  0 X^2 X^2  0 X^2  0  0 X^2  0  0 X^2  0 X^2  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0
 0  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0  0  0  0  0 X^2  0  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0  0  0  0  0 X^2  0
 0  0  0  0  0  0  0 X^2  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2  0  0  0  0 X^2 X^2  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+42x^44+54x^45+124x^46+148x^47+191x^48+234x^49+319x^50+388x^51+398x^52+456x^53+351x^54+342x^55+268x^56+224x^57+169x^58+124x^59+100x^60+50x^61+48x^62+20x^63+20x^64+6x^65+7x^66+4x^68+5x^70+2x^71+1x^74

The gray image is a linear code over GF(2) with n=212, k=12 and d=88.
This code was found by Heurico 1.16 in 1 seconds.