The generator matrix

 1  0  0  1  1  1  X  1  1  1  1 X^2+X+2  0  2 X^2+2  1  1  1 X^2+X  1  1 X^2+X  1 X+2 X+2  1  1  1  1 X^2 X^2  1  1 X^2+2  0  X  2  0 X^2+X X+2  X
 0  1  0  0 X^2+1 X+3  1 X^2+X+3 X^2+X X^2+X+3 X^2  X X^2+2  1  1  2  1  3 X+2  0  1  1 X^2+3  1 X^2+2  1 X^2+X X^2+2 X+2 X+2  1 X+1  X  1  1  1  1  1  1 X^2+X  1
 0  0  1  1  1 X^2 X^2+1 X+3  3 X^2+X+2 X+2  1  1 X+2 X^2+X+1 X^2+2  0 X^2+X+3  1 X+3 X^2+1  X  0 X+3  1 X^2+X+3 X+2 X^2 X+3  1  1  2  1 X^2+3  0 X^2  3 X^2+X+3 X^2+X  1 X^2+2
 0  0  0  X X+2  2 X+2 X^2+X+2  X X^2+2 X^2 X^2+X+2 X^2+X+2 X+2 X^2+2 X^2+X X+2  2  2 X^2 X^2+2  2 X^2 X+2 X^2+X  X X^2+X  X  0 X^2+2 X+2  X  2 X^2 X^2+2 X^2+2 X^2+X X^2 X+2 X^2 X^2+X+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+582x^36+1144x^37+3004x^38+3632x^39+5578x^40+5200x^41+5348x^42+3904x^43+2608x^44+888x^45+644x^46+80x^47+125x^48+28x^50+2x^52

The gray image is a code over GF(2) with n=328, k=15 and d=144.
This code was found by Heurico 1.16 in 677 seconds.