The generator matrix

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

generates a code of length 38 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+69x^34+144x^35+426x^36+214x^37+518x^38+156x^39+253x^40+80x^41+108x^42+36x^43+24x^44+10x^45+8x^46+1x^58

The gray image is a code over GF(2) with n=304, k=11 and d=136.
This code was found by Heurico 1.16 in 0.078 seconds.