The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  2  2  1 X^2  1
 0  X  0  X  2  0 X+2  X X^2 X^2+X X^2 X^2+X X^2+2 X^2 X^2+X+2 X^2+X  0  2  X X+2 X^2  0 X^2+X+2 X^2+2 X^2+X X^2  X X^2+X X+2 X^2  X  2 X^2+2 X^2+X+2 X+2  X X^2+2  X X^2+X+2  X X^2+X+2
 0  0  X  X X^2 X^2+X X^2+X X^2 X^2 X^2+X+2  X  2  0 X^2+X X+2 X^2+2  2 X^2+X+2 X+2  0  2 X+2 X^2+X X^2  0 X+2 X^2+X X+2 X^2 X^2+X+2 X^2+2  2 X^2+X  X X+2  2  X X^2  0 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 38.

Homogenous weight enumerator: w(x)=1x^0+74x^38+120x^39+174x^40+324x^41+154x^42+82x^43+65x^44+16x^45+11x^46+2x^47+1x^74

The gray image is a code over GF(2) with n=328, k=10 and d=152.
This code was found by Heurico 1.16 in 0.032 seconds.