The generator matrix

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

generates a code of length 39 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+34x^37+78x^38+284x^39+78x^40+34x^41+1x^44+1x^50+1x^62

The gray image is a code over GF(2) with n=312, k=9 and d=148.
This code was found by Heurico 1.16 in 0.016 seconds.