The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X 2X+2  1  2  1  1  1 2X+2  1  X  1  1  2  1  1  1 2X+2  X  X  X  1
 0  X  0  X 2X  0 X+2 3X+2  0 2X 3X 3X  0 2X+2 3X+2  X 2X+2  X  0 2X+2  X  2 3X+2 2X+2 2X 3X X+2 2X  X 3X  2  2  X 3X+2 3X 2X  0
 0  0  X  X  0 3X+2 X+2 2X  2 3X+2 3X+2  2 2X+2  X  2  X 3X 3X+2 3X  X X+2 2X 2X  X X+2 2X 3X+2 X+2  X  0 X+2 3X+2  2 3X+2  2 X+2 2X
 0  0  0  2 2X+2  2 2X  2  2  0  2 2X+2  0 2X+2  0 2X 2X  0 2X+2  0  0  0 2X  2 2X+2 2X  2 2X 2X+2 2X+2 2X  0 2X+2 2X+2  2  2 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+45x^32+196x^33+336x^34+538x^35+602x^36+794x^37+583x^38+442x^39+266x^40+140x^41+68x^42+58x^43+14x^44+6x^45+4x^46+2x^47+1x^54

The gray image is a code over GF(2) with n=296, k=12 and d=128.
This code was found by Heurico 1.16 in 0.171 seconds.