The generator matrix

 1  0  0  1  1  1 X+2  X  1 X^2+X+2  1  1  0  1  2  1 X^2+X  1  1 X^2  1 X+2  1  1  1  1  0  1  1  1  X X+2 X+2  1  1  1  1
 0  1  0  0 X^2+3 X+1  1  2 X^2+X+1  1 X^2+X+2 X^2+X  1  3 X^2+X X^2  1 X^2+X+3  X  1 X+2 X+2 X^2+X+1 X^2+X+2 X+2  1  1  1 X^2+2 X+3  1  1  1 X+3 X^2+X+2 X^2+X+2  2
 0  0  1 X+1 X+1  0 X^2+X+1  1 X^2+X+1 X^2+X X^2+X X+1 X+3 X^2+X  1  3  2 X^2+X+2 X^2+3 X^2+3 X+2  1 X^2+2  0 X^2+X+3 X^2+2  X  3 X^2+X+1 X^2+3 X^2+3 X+2  X X^2+X+2  3 X^2+1  0
 0  0  0 X^2 X^2+2  2 X^2 X^2  2 X^2 X^2+2  2  2  0  0 X^2  0 X^2  0 X^2+2  2 X^2+2 X^2 X^2 X^2+2  0 X^2  2  0 X^2+2 X^2  2  0 X^2  2 X^2+2 X^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+85x^32+684x^33+1217x^34+2272x^35+2344x^36+3358x^37+2288x^38+2246x^39+1041x^40+596x^41+165x^42+40x^43+14x^44+18x^45+10x^46+2x^47+3x^48

The gray image is a code over GF(2) with n=296, k=14 and d=128.
This code was found by Heurico 1.16 in 1.3 seconds.