The generator matrix

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

generates a code of length 37 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+383x^32+1244x^33+2572x^34+3592x^35+5948x^36+5420x^37+5906x^38+3760x^39+2396x^40+948x^41+360x^42+136x^43+84x^44+4x^45+10x^46+4x^48

The gray image is a code over GF(2) with n=296, k=15 and d=128.
This code was found by Heurico 1.16 in 16.5 seconds.