The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+27x^32+100x^33+251x^34+124x^35+240x^36+632x^37+44x^38+432x^39+44x^40+92x^41+20x^42+20x^43+8x^44+8x^45+4x^46+1x^66

The gray image is a code over GF(2) with n=296, k=11 and d=128.
This code was found by Heurico 1.16 in 0.078 seconds.