The generator matrix

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

generates a code of length 44 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+84x^37+897x^38+2666x^39+5295x^40+10258x^41+14536x^42+20424x^43+21520x^44+21974x^45+15233x^46+9844x^47+4794x^48+2322x^49+830x^50+216x^51+102x^52+46x^53+24x^54+2x^55+4x^57

The gray image is a code over GF(2) with n=352, k=17 and d=148.
This code was found by Heurico 1.16 in 83.3 seconds.