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

generates a code of length 47 over Z2[X]/(X^3) who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+74x^37+185x^38+238x^39+302x^40+442x^41+437x^42+638x^43+1068x^44+1504x^45+2272x^46+2352x^47+1784x^48+1610x^49+1212x^50+638x^51+464x^52+376x^53+279x^54+216x^55+152x^56+84x^57+31x^58+12x^59+4x^60+6x^61+2x^63+1x^80

The gray image is a linear code over GF(2) with n=188, k=14 and d=74.
This code was found by Heurico 1.16 in 13.1 seconds.