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

generates a code of length 47 over Z2[X]/(X^3) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+55x^40+64x^41+88x^42+140x^43+158x^44+196x^45+243x^46+252x^47+216x^48+192x^49+129x^50+104x^51+49x^52+52x^53+41x^54+12x^55+28x^56+8x^57+10x^58+4x^59+5x^60+1x^74

The gray image is a linear code over GF(2) with n=188, k=11 and d=80.
This code was found by Heurico 1.16 in 0.252 seconds.