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

generates a code of length 47 over Z2[X]/(X^4) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+54x^42+88x^43+101x^44+128x^45+530x^46+272x^47+542x^48+64x^49+114x^50+88x^51+55x^52+6x^54+4x^56+1x^88

The gray image is a linear code over GF(2) with n=376, k=11 and d=168.
This code was found by Heurico 1.16 in 0.141 seconds.