The generator matrix

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

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+329x^40+216x^41+568x^42+640x^43+783x^44+384x^45+608x^46+288x^47+218x^48+8x^49+32x^50+5x^52+8x^54+8x^56

The gray image is a code over GF(2) with n=352, k=12 and d=160.
This code was found by Heurico 1.16 in 0.172 seconds.