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.