The generator matrix

 1  0  1  1  1  X  1  1 X^2+X+2  1  1 X^2+X X^2+X+2 X^2  1  1  1  1 X^2+X+2  1 X^2  1  X  1  1  1  1  X  0 X^2+2 X+2  0 X^2  1 X^2+2 X^2  1  1  1  1  1
 0  1  1 X^2 X+1  1  X  3  1 X+2 X^2+X+1  1  1  1 X^2 X^2+3 X+2 X+1  1  2  1 X^2+X+3  1  X  3  0 X^2+X+1  1  1  1  1  1  1 X^2+X  1  1 X^2+3 X^2+2 X^2+X+2  0  0
 0  0  X X+2  2 X+2 X+2  2 X^2+X+2  0  X  0 X^2+2 X^2 X^2+X+2 X^2+2 X^2+X+2 X^2  X X^2+2 X+2 X^2+X X^2+X+2 X^2+2 X^2+X X^2+X X^2+2  0 X^2+X  2 X^2+2 X+2 X^2+2 X^2+X+2 X^2+X+2 X^2+X X^2+X X^2  0  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+220x^38+312x^39+422x^40+220x^41+358x^42+292x^43+184x^44+4x^45+16x^46+4x^47+9x^48+4x^50+1x^54+1x^62

The gray image is a code over GF(2) with n=328, k=11 and d=152.
This code was found by Heurico 1.16 in 0.063 seconds.