The generator matrix

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

generates a code of length 38 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+158x^34+228x^35+789x^36+430x^37+952x^38+402x^39+758x^40+204x^41+134x^42+8x^43+9x^44+6x^45+10x^46+2x^47+3x^48+2x^54

The gray image is a code over GF(2) with n=304, k=12 and d=136.
This code was found by Heurico 1.16 in 8.41 seconds.