The generator matrix

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

generates a code of length 37 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+290x^35+84x^36+408x^37+16x^38+108x^39+24x^40+88x^41+2x^43+3x^48

The gray image is a code over GF(2) with n=296, k=10 and d=140.
This code was found by Heurico 1.16 in 10 seconds.