The generator matrix

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

generates a code of length 41 over Z4[X]/(X^2+2X+2) 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.