The generator matrix

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

generates a code of length 37 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+268x^34+228x^35+432x^36+296x^37+394x^38+136x^39+205x^40+40x^41+32x^42+4x^43+8x^44+2x^46+2x^52

The gray image is a code over GF(2) with n=296, k=11 and d=136.
This code was found by Heurico 1.16 in 6.03 seconds.