The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 0 X X^2+2 X 2 X X^2 1 1 1 1 X X X X 1 1 1 1 X^2 X^2 0 2 1 1 1 1
0 X X^2+2 X^2+X 2 X^2+X+2 X^2 X+2 0 X^2+X X^2+2 X+2 2 X^2+X+2 X^2 X X^2+X X X+2 X X^2+X+2 X X X 0 X^2+2 2 X^2 0 X^2+2 2 X^2 X^2+X X+2 X^2+X+2 X X^2+2 X^2 X^2 X^2 0 2 X^2+X X^2+X+2
generates a code of length 44 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 44.
Homogenous weight enumerator: w(x)=1x^0+118x^44+4x^46+4x^50+1x^56
The gray image is a code over GF(2) with n=352, k=7 and d=176.
This code was found by Heurico 1.16 in 0.031 seconds.