The generator matrix

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

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+90x^38+702x^39+1451x^40+2720x^41+3992x^42+4760x^43+5144x^44+5290x^45+3969x^46+2460x^47+1278x^48+620x^49+154x^50+74x^51+46x^52+10x^53+3x^54+2x^55+2x^59

The gray image is a code over GF(2) with n=352, k=15 and d=152.
This code was found by Heurico 1.16 in 6.22 seconds.