The generator matrix

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

generates a code of length 41 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+46x^34+732x^35+2330x^36+4928x^37+9511x^38+15718x^39+20347x^40+23026x^41+21192x^42+16354x^43+9432x^44+4558x^45+1923x^46+644x^47+208x^48+78x^49+28x^50+6x^51+2x^53+4x^54+2x^55+2x^56

The gray image is a code over GF(2) with n=328, k=17 and d=136.
This code was found by Heurico 1.16 in 79.6 seconds.