The generator matrix

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

generates a code of length 39 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+112x^35+115x^36+326x^37+289x^38+454x^39+271x^40+268x^41+52x^42+92x^43+29x^44+14x^45+9x^46+14x^47+1x^54+1x^62

The gray image is a code over GF(2) with n=312, k=11 and d=140.
This code was found by Heurico 1.16 in 2.52 seconds.