The generator matrix

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

generates a code of length 41 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+159x^36+728x^37+1447x^38+1968x^39+2530x^40+2834x^41+2575x^42+2002x^43+1208x^44+584x^45+221x^46+60x^47+35x^48+10x^49+13x^50+2x^51+1x^52+4x^53+2x^56

The gray image is a code over GF(2) with n=328, k=14 and d=144.
This code was found by Heurico 1.16 in 1.5 seconds.