The generator matrix

 1  0  1  1  1 X^2+X+2  X  1  1 X^2+2  1  1  1  1  1 X^2+X+2  1  2  1 X^2+X  1  1  1  1  1  1 X+2  1 X^2  1  1  1 X+2 X^2+2 X^2+2  1  1
 0  1 X+1 X^2+X X^2+3  1  1  2 X^2+1  1 X^2+X+1 X^2+X+2  3 X+2 X+1  1 X^2+2  1 X^2+X+1  1 X^2  1  X X^2+1 X^2 X^2+3  1 X+1  1 X^2+X X+2 X^2+X  1  1  1 X+1  0
 0  0 X^2  0 X^2+2 X^2 X^2+2 X^2  2  0 X^2+2 X^2  2  0  2 X^2  0 X^2+2 X^2+2  0 X^2+2 X^2 X^2  2 X^2+2 X^2  0  0 X^2+2  0  2  2  2  2  0  0  0
 0  0  0  2  0  0  2  0  2  2  2  2  2  2  0  0  0  2  2  0  2  2  0  0  2  0  0  2  0  0  0  2  2  0  0  0  0
 0  0  0  0  2  0  2  2  0  2  2  0  2  2  2  2  2  0  0  2  2  2  2  0  0  0  0  2  0  2  0  2  2  2  2  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+21x^32+178x^33+260x^34+600x^35+557x^36+892x^37+550x^38+592x^39+247x^40+158x^41+18x^42+4x^43+3x^44+4x^45+2x^46+4x^47+3x^48+2x^50

The gray image is a code over GF(2) with n=296, k=12 and d=128.
This code was found by Heurico 1.16 in 0.141 seconds.