The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 X 1 1 1 X 1 X X X X^2 0 X^2 X^3 X X X^2 1 1 X X 1 1 X^2 X X 1 1
0 X^3+X^2 X^3 X^2 0 X^3+X^2 X^3 X^2 0 X^3+X^2 X^3 X^2 0 X^3+X^2 X^3+X^2 X^3 X^2 X^2 0 X^3 X^3+X^2 X^3+X^2 X^2 0 X^3 X^2 X^3+X^2 X^2 X^2 X^2 0 X^3 X^3 0 X^3 X^3+X^2 X^2 X^3+X^2 X^2 0 0 X^3 0 X^3
generates a code of length 44 over Z2[X]/(X^4) who´s minimum homogenous weight is 44.
Homogenous weight enumerator: w(x)=1x^0+49x^44+10x^46+1x^48+2x^50+1x^52
The gray image is a linear code over GF(2) with n=352, k=6 and d=176.
This code was found by Heurico 1.16 in 0.047 seconds.