The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+87x^40+180x^41+239x^42+404x^43+333x^44+360x^45+202x^46+84x^47+74x^48+44x^49+22x^50+16x^51+1x^52+1x^74

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 0.093 seconds.