The generator matrix

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

generates a code of length 44 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+186x^39+701x^40+1590x^41+2082x^42+2510x^43+2532x^44+2528x^45+1905x^46+1314x^47+582x^48+268x^49+112x^50+38x^51+6x^52+12x^53+13x^54+2x^56+2x^57

The gray image is a code over GF(2) with n=352, k=14 and d=156.
This code was found by Heurico 1.16 in 1.77 seconds.