The generator matrix

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

generates a code of length 38 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+64x^35+142x^36+128x^37+480x^38+142x^40+64x^43+2x^44+1x^64

The gray image is a code over GF(2) with n=304, k=10 and d=140.
This code was found by Heurico 1.16 in 32.2 seconds.