The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+118x^37+149x^38+220x^39+372x^40+392x^41+365x^42+190x^43+120x^44+62x^45+9x^46+32x^47+2x^48+4x^49+3x^50+6x^51+2x^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 3.47 seconds.