The generator matrix

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

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+70x^33+61x^34+140x^35+148x^36+442x^37+377x^38+450x^39+123x^40+118x^41+31x^42+34x^43+12x^44+6x^45+11x^46+14x^47+3x^48+4x^49+2x^51+1x^56

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 4.91 seconds.