The generator matrix

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

generates a code of length 44 over Z2[X]/(X^4) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+380x^42+260x^44+380x^46+1x^56+2x^60

The gray image is a linear code over GF(2) with n=352, k=10 and d=168.
This code was found by Heurico 1.16 in 0.078 seconds.