The generator matrix

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

generates a code of length 41 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+480x^38+652x^39+806x^40+692x^41+460x^42+380x^43+329x^44+124x^45+156x^46+8x^47+7x^48+1x^52

The gray image is a code over GF(2) with n=328, k=12 and d=152.
This code was found by Heurico 1.16 in 0.843 seconds.