The generator matrix

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

generates a code of length 39 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 33.

Homogenous weight enumerator: w(x)=1x^0+584x^33+2094x^34+4806x^35+9290x^36+15626x^37+20922x^38+23884x^39+21632x^40+16042x^41+9110x^42+4456x^43+1766x^44+574x^45+190x^46+68x^47+15x^48+6x^49+4x^50+2x^51

The gray image is a code over GF(2) with n=312, k=17 and d=132.
This code was found by Heurico 1.16 in 79.3 seconds.