The generator matrix

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

generates a code of length 39 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+240x^36+232x^37+504x^38+184x^39+450x^40+216x^41+152x^42+8x^43+50x^44+9x^48+2x^52

The gray image is a code over GF(2) with n=312, k=11 and d=144.
This code was found by Heurico 1.16 in 0.14 seconds.