The generator matrix

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

generates a code of length 44 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+35x^38+154x^39+166x^40+366x^41+383x^42+662x^43+617x^44+618x^45+444x^46+350x^47+91x^48+130x^49+30x^50+10x^51+15x^52+6x^53+2x^54+8x^55+4x^56+1x^58+2x^60+1x^62

The gray image is a code over GF(2) with n=352, k=12 and d=152.
This code was found by Heurico 1.16 in 0.297 seconds.