The generator matrix

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

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+127x^32+584x^33+1218x^34+2304x^35+2385x^36+3336x^37+2500x^38+2088x^39+919x^40+570x^41+242x^42+72x^43+23x^44+4x^45+8x^46+1x^48+2x^49

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 1.41 seconds.