The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^3+X  1  1 X^3+X^2  1  1 X^3+X^2  1  1 X^3+X  1  1  1  1  0 X^2+X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 X^3 X^3+X^2+X  X  1
 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^2+1  1 X^3+X^2 X^3+X X^3+X^2+X+1 X^3+1  1  1 X^3 X^3+X^2+X X^2  X X^3+X+1 X^3+X^2+1 X^2+X+1  1 X^3 X^3+X^2+X X^2  X X^3+X+1 X^3+X^2+1 X^2+X+1  1  1  1  0  0
 0  0 X^3 X^3  0 X^3 X^3  0  0  0 X^3 X^3 X^3  0  0  0 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3  0  0 X^3 X^3  0  0 X^3  0 X^3 X^3  0  0 X^3 X^3  0 X^3  0  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+46x^42+50x^43+286x^44+108x^45+16x^46+2x^47+1x^52+1x^54+1x^66

The gray image is a linear code over GF(2) with n=352, k=9 and d=168.
This code was found by Heurico 1.16 in 0.032 seconds.