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

generates a code of length 37 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+51x^32+224x^35+512x^37+43x^38+128x^39+12x^40+32x^43+20x^46+1x^70

The gray image is a code over GF(2) with n=296, k=10 and d=128.
This code was found by Heurico 1.16 in 0.047 seconds.