The generator matrix

 1  0  0  1  1  1 X+2 3X+2  1  0  1  1  1  2  1  1  1  1 3X+2 X+2  1 3X  0  X X+2 3X 3X+2 2X+2  1  1  1  1 2X+2  1 2X+2 3X  1
 0  1  0  0 2X+3 X+1  1 2X X+3  1  X 3X 3X+1  1 2X 2X+3  2  1  X  1  X  1  1  X  0  1  1  1 2X+2 2X+2 3X+3  X  1  2  1  1 2X
 0  0  1 X+1 X+1  0 X+3  1 X+3  3  1  X X+2  X  X  2 2X+1  1  1 3X+2 2X+2 X+2 X+1  1  1 3X+3 2X  0 X+1 3X  2 3X+1 2X+3  1 2X+2 X+1 2X
 0  0  0  2 2X+2 2X  2  2  0 2X 2X  2 2X+2  0 2X  0 2X  2 2X+2 2X  2 2X+2  2  0 2X  0  2  2 2X 2X+2  2 2X+2 2X+2  2 2X  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+116x^32+644x^33+1245x^34+2012x^35+2781x^36+3042x^37+2612x^38+2024x^39+1063x^40+532x^41+204x^42+58x^43+39x^44+6x^45+3x^50+2x^51

The gray image is a code over GF(2) with n=296, k=14 and d=128.
This code was found by Heurico 1.16 in 1.36 seconds.