The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+430x^31+1963x^32+4752x^33+8880x^34+14968x^35+21713x^36+24936x^37+22442x^38+15726x^39+8631x^40+4176x^41+1756x^42+518x^43+135x^44+24x^45+10x^46+4x^47+5x^48+2x^51

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 72.5 seconds.