The generator matrix

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

generates a code of length 37 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+458x^31+1803x^32+4618x^33+9412x^34+14782x^35+22312x^36+23620x^37+22954x^38+15750x^39+8974x^40+3964x^41+1722x^42+498x^43+132x^44+52x^45+6x^46+10x^48+2x^49+2x^50

The gray image is a code over GF(2) with n=296, k=17 and d=124.
This code was found by Heurico 1.16 in 69.6 seconds.