The generator matrix

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

generates a code of length 44 over Z4[X]/(X^3+2,2X) 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 code over GF(2) with n=352, k=10 and d=168.
This code was found by Heurico 1.16 in 0.093 seconds.