The generator matrix

 1  0  0  0  1  1  1 X^2  1  1 X+2 X^2+X+2  1 X+2  1 X^2  2 X^2+X+2  1  1  2  1  1 X^2  1  1  1  1  1  X X^2+2 X^2+X+2 X^2  1 X+2  1  1
 0  1  0  0 X^2  3  1  1 X^2+1  3 X^2+2  1 X+2  1  2 X+2  1  0 X+3 X^2+X+2  1  X X^2+X+1  1  1 X^2+2 X^2+3  1 X^2+X+2 X^2  1  1  1  X  1 X+1  0
 0  0  1  0 X^2+1  1 X^2 X^2+1 X+1 X^2+X  1 X+2 X^2+3 X+3 X^2+X+2  1 X+3  1  2 X^2+X+1 X^2+3  2  2 X^2+X+2 X+1 X^2+1  X X^2+X X+2  0 X^2+2 X^2+2 X+1  X X^2+X+1 X^2+X+1  0
 0  0  0  1  1 X^2 X^2+1  3 X+1 X^2+X  3  3  X X+2 X^2+1 X+3 X^2 X^2  X X+3 X^2+X+1 X+3  3 X^2+X+1  1 X^2+X+3  3 X^2+2 X^2  1 X+3 X^2+2 X^2+X  1  2 X^2+X  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+176x^31+988x^32+2802x^33+4373x^34+8086x^35+10248x^36+12046x^37+10536x^38+8068x^39+4501x^40+2514x^41+797x^42+310x^43+38x^44+44x^45+6x^46+2x^53

The gray image is a code over GF(2) with n=296, k=16 and d=124.
This code was found by Heurico 1.16 in 19 seconds.