The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2+2  1  1 X+2  1  1  0  1  1 X^2+X  1  1 X^2+2  1  1 X^2+X X+2  0  0 X^2+2 X^2+X X^2 X^2+X+2  2 X^2+2  1  X  1  1  1  X  1  0
 0  1 X+1 X^2+X X^2+1  1 X^2+X+3 X^2+2  1 X+2  3  1  0 X+1  1 X^2+X X^2+1  1 X^2+2 X^2+X+3  1 X+2  3  1  1  X  1  1  1  1  1  1  X  0 X^2+2 X^2+X X+2 X+1 X+2 X^2+1  1
 0  0  2  0  0  0  0  2  2  2  2  2  0  0  0  0  0  0  2  2  2  2  2  2  0  2  0  0  2  0  2  2  0  0  0  2  0  2  2  0  0
 0  0  0  2  0  2  2  2  2  0  2  0  2  0  2  0  2  0  0  2  0  2  0  2  0  0  2  0  2  2  0  0  2  0  0  2  0  2  2  2  0
 0  0  0  0  2  0  2  2  2  2  0  2  0  2  0  0  2  0  2  0  2  2  0  2  2  0  2  0  0  0  0  2  2  2  2  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+84x^37+156x^38+282x^39+312x^40+436x^41+274x^42+272x^43+129x^44+56x^45+17x^46+22x^47+4x^48+1x^52+1x^54+1x^64

The gray image is a code over GF(2) with n=328, k=11 and d=148.
This code was found by Heurico 1.16 in 0.063 seconds.