The generator matrix

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

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+6x^42+80x^43+76x^44+80x^45+8x^46+3x^48+1x^50+1x^66

The gray image is a linear code over GF(2) with n=352, k=8 and d=168.
This code was found by Heurico 1.16 in 0.063 seconds.