The generator matrix

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

generates a code of length 37 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+412x^31+1910x^32+4600x^33+9121x^34+15040x^35+22408x^36+23896x^37+22732x^38+15178x^39+9109x^40+4362x^41+1641x^42+486x^43+134x^44+20x^45+10x^46+2x^47+6x^48+2x^49+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 75.5 seconds.