The generator matrix

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

generates a code of length 38 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 33.

Homogenous weight enumerator: w(x)=1x^0+50x^33+100x^34+162x^35+100x^36+564x^37+144x^38+564x^39+78x^40+148x^41+57x^42+36x^43+12x^44+4x^45+16x^46+4x^47+1x^48+2x^49+2x^50+2x^51+1x^58

The gray image is a code over GF(2) with n=304, k=11 and d=132.
This code was found by Heurico 1.16 in 39.5 seconds.