The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X 2X  1  1  1  1  X  1  1  1  0  1  1  1 2X+2  1  1  1  1 2X+2  1  1  0  1  0
 0  X  0 3X+2 2X+2 X+2  2  X 2X+2 3X+2  0 3X+2 2X 3X 2X+2  X 3X+2  X  0 3X+2  2 3X 2X X+2  0 2X+2  X 3X X+2  0  X X+2 2X+2  0  2 2X+2  X 2X  X  2  X
 0  0  2  0 2X+2 2X+2 2X 2X+2 2X+2  0 2X  2 2X+2 2X+2 2X 2X  0  2  0  0 2X 2X  2 2X+2  2  2  0  2  2 2X+2 2X+2 2X  2  2  2 2X+2 2X+2 2X  0  0 2X
 0  0  0 2X  0  0 2X 2X 2X  0 2X 2X 2X  0  0 2X 2X 2X  0 2X 2X  0  0  0  0 2X  0 2X 2X 2X  0  0  0 2X  0 2X 2X  0  0 2X 2X
 0  0  0  0 2X  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X  0  0 2X 2X 2X 2X  0 2X 2X  0  0 2X 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+136x^37+117x^38+262x^39+263x^40+536x^41+307x^42+220x^43+48x^44+82x^45+23x^46+30x^47+7x^48+12x^49+2x^53+1x^56+1x^66

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 0.453 seconds.