The generator matrix

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

generates a code of length 44 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+104x^37+836x^38+2808x^39+5143x^40+9780x^41+15231x^42+20622x^43+21900x^44+20854x^45+15268x^46+10004x^47+4934x^48+2362x^49+881x^50+256x^51+50x^52+18x^53+6x^54+4x^55+4x^56+2x^57+2x^58+2x^59

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 86.6 seconds.