The generator matrix

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

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+122x^35+153x^36+210x^37+369x^38+388x^39+370x^40+196x^41+94x^42+78x^43+32x^44+22x^45+1x^46+4x^47+3x^48+4x^49+1x^60

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 1.45 seconds.