The generator matrix

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

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+680x^35+2369x^36+5300x^37+9140x^38+15570x^39+20269x^40+23936x^41+20701x^42+16358x^43+8982x^44+4688x^45+2046x^46+726x^47+216x^48+56x^49+17x^50+10x^51+3x^52+4x^53

The gray image is a code over GF(2) with n=328, k=17 and d=140.
This code was found by Heurico 1.16 in 104 seconds.