The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+182x^34+360x^35+340x^36+428x^37+268x^38+244x^39+119x^40+52x^41+34x^42+4x^43+10x^44+4x^46+2x^48

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 0.047 seconds.