The generator matrix

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

generates a code of length 44 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+44x^41+242x^42+172x^43+188x^44+118x^45+165x^46+32x^47+40x^48+18x^49+1x^50+1x^52+2x^56

The gray image is a code over GF(2) with n=352, k=10 and d=164.
This code was found by Heurico 1.16 in 0.047 seconds.