The generator matrix

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

generates a code of length 44 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+198x^40+96x^41+132x^42+352x^43+504x^44+288x^45+248x^46+32x^47+184x^48+4x^50+8x^52+1x^80

The gray image is a code over GF(2) with n=352, k=11 and d=160.
This code was found by Heurico 1.16 in 0.125 seconds.