The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  1  X  1  1  1  1  1  1  X  X  1  1
 0 2X  0  0  0  0  0  0  0  0 2X 2X  0  0  0 2X  0  0  0  0 2X 2X 2X 2X  0 2X 2X 2X 2X  0 2X 2X 2X 2X  0 2X 2X 2X 2X 2X 2X
 0  0 2X  0  0  0  0  0  0 2X 2X 2X  0 2X 2X  0  0  0 2X 2X 2X 2X 2X 2X  0  0 2X  0  0  0 2X 2X  0  0 2X  0 2X  0 2X  0 2X
 0  0  0 2X  0  0  0  0  0 2X  0 2X 2X 2X  0 2X  0 2X 2X  0  0  0  0  0 2X 2X  0  0  0 2X 2X  0  0 2X 2X  0 2X 2X 2X  0 2X
 0  0  0  0 2X  0  0  0 2X  0  0 2X 2X  0 2X 2X  0  0 2X 2X  0  0  0 2X 2X 2X 2X 2X  0 2X  0  0  0  0 2X 2X 2X  0  0 2X  0
 0  0  0  0  0 2X  0  0 2X  0 2X  0  0 2X 2X 2X  0 2X 2X  0  0  0  0 2X 2X  0  0  0 2X 2X 2X 2X  0  0 2X 2X  0 2X  0 2X 2X
 0  0  0  0  0  0 2X  0 2X 2X 2X  0  0  0 2X 2X 2X  0  0 2X  0  0 2X  0 2X 2X 2X  0  0  0 2X 2X  0 2X 2X 2X 2X 2X 2X  0  0
 0  0  0  0  0  0  0 2X 2X 2X  0  0 2X 2X 2X  0 2X  0 2X  0  0 2X 2X  0  0 2X  0 2X  0  0  0 2X 2X 2X  0  0 2X  0  0 2X 2X

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+34x^34+54x^36+71x^38+116x^40+1536x^41+98x^42+58x^44+36x^46+17x^48+12x^50+8x^52+5x^54+1x^56+1x^72

The gray image is a code over GF(2) with n=328, k=11 and d=136.
This code was found by Heurico 1.16 in 47.5 seconds.