The generator matrix

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

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+160x^32+388x^36+1024x^37+256x^38+175x^40+12x^44+31x^48+1x^56

The gray image is a code over GF(2) with n=296, k=11 and d=128.
This code was found by Heurico 1.16 in 57.3 seconds.