The generator matrix

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

generates a code of length 41 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+228x^37+876x^38+1256x^39+1246x^40+1312x^41+1247x^42+858x^43+660x^44+298x^45+114x^46+62x^47+13x^48+18x^49+3x^50

The gray image is a code over GF(2) with n=328, k=13 and d=148.
This code was found by Heurico 1.16 in 0.375 seconds.