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

generates a code of length 53 over Z2[X]/(X^3) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+47x^42+104x^43+200x^44+290x^45+378x^46+542x^47+618x^48+896x^49+1240x^50+1432x^51+1514x^52+1678x^53+1825x^54+1478x^55+1146x^56+826x^57+674x^58+562x^59+287x^60+248x^61+162x^62+100x^63+59x^64+30x^65+22x^66+6x^67+14x^68+3x^70+1x^74+1x^76

The gray image is a linear code over GF(2) with n=212, k=14 and d=84.
This code was found by Heurico 1.16 in 15.2 seconds.