The generator matrix

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

generates a code of length 52 over Z2[X]/(X^3) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+79x^42+100x^43+386x^44+672x^45+1039x^46+1498x^47+1947x^48+2444x^49+2904x^50+3502x^51+3500x^52+3508x^53+3177x^54+2516x^55+2018x^56+1392x^57+873x^58+516x^59+306x^60+164x^61+111x^62+58x^63+34x^64+12x^65+8x^66+2x^67+1x^70

The gray image is a linear code over GF(2) with n=208, k=15 and d=84.
This code was found by Heurico 1.16 in 33.7 seconds.