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

generates a code of length 37 over Z4[X]/(X^3+2,2X) 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.