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

generates a code of length 37 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 33.

Homogenous weight enumerator: w(x)=1x^0+34x^33+42x^34+28x^35+282x^36+272x^37+280x^38+20x^39+19x^40+14x^41+14x^42+16x^43+1x^44+1x^68

The gray image is a code over GF(2) with n=296, k=10 and d=132.
This code was found by Heurico 1.16 in 0.047 seconds.