The generator matrix

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

generates a code of length 41 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+326x^34+1684x^35+4311x^36+9832x^37+18383x^38+30830x^39+40920x^40+47742x^41+43114x^42+31504x^43+18386x^44+9208x^45+3570x^46+1630x^47+467x^48+158x^49+44x^50+16x^51+11x^52+4x^53+3x^54

The gray image is a code over GF(2) with n=328, k=18 and d=136.
This code was found by Heurico 1.16 in 321 seconds.