The generator matrix

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

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+64x^37+153x^38+374x^39+279x^40+488x^41+202x^42+252x^43+70x^44+64x^45+45x^46+30x^47+17x^48+8x^49+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 0.094 seconds.