The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  X  1  1  1  1  1  1 X^2  1  1  1  1  1  0  X  1  1 X^2  1  X  1  1
 0 X^3+X^2  0 X^3+X^2  0 X^3+X^2  0 X^2 X^3 X^3+X^2  0 X^3+X^2  0 X^3+X^2  0 X^2 X^3 X^3+X^2 X^3+X^2  0 X^2 X^3 X^2 X^3  0 X^3+X^2 X^2 X^3+X^2  0  0 X^3 X^3 X^3+X^2  0 X^3  0 X^3  0 X^2 X^3+X^2  0 X^3 X^3+X^2 X^3+X^2  0 X^3  0
 0  0 X^3  0  0  0  0  0 X^3  0  0  0 X^3  0 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3  0  0 X^3  0  0 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3  0
 0  0  0 X^3  0  0  0 X^3  0  0  0 X^3  0  0 X^3  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0  0 X^3  0 X^3  0 X^3  0 X^3  0 X^3  0 X^3  0
 0  0  0  0 X^3  0  0  0  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0  0 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0  0 X^3  0  0  0  0 X^3  0
 0  0  0  0  0 X^3  0 X^3  0 X^3 X^3  0 X^3  0 X^3  0  0  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0  0  0 X^3  0 X^3 X^3 X^3 X^3  0  0 X^3  0 X^3  0  0 X^3  0  0 X^3  0
 0  0  0  0  0  0 X^3  0 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0  0  0  0  0 X^3 X^3  0 X^3  0 X^3  0  0 X^3  0 X^3  0 X^3  0  0 X^3  0 X^3  0  0 X^3 X^3  0

generates a code of length 47 over Z2[X]/(X^4) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+26x^40+71x^42+153x^44+128x^45+531x^46+256x^47+524x^48+128x^49+141x^50+52x^52+20x^54+6x^56+3x^58+3x^60+1x^62+2x^64+1x^66+1x^80

The gray image is a linear code over GF(2) with n=376, k=11 and d=160.
This code was found by Heurico 1.16 in 0.156 seconds.