The generator matrix

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

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+202x^36+344x^37+389x^38+336x^39+310x^40+220x^41+133x^42+56x^43+34x^44+4x^45+13x^46+4x^48+1x^50+1x^56

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 0.063 seconds.