The generator matrix

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

generates a code of length 41 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+168x^35+1180x^36+2742x^37+4868x^38+7798x^39+10237x^40+11386x^41+10690x^42+7978x^43+4586x^44+2306x^45+1069x^46+370x^47+124x^48+14x^49+12x^50+6x^51+1x^54

The gray image is a code over GF(2) with n=328, k=16 and d=140.
This code was found by Heurico 1.16 in 19.8 seconds.