The generator matrix

 1  0  0  0  1  1  1  1  2  1  X  1  1  2 X+2  2  1  1 X^2+2  1 X^2+2 X^2+X X+2  1  1  1 X+2 X+2  0  1  1  1  1  2  1 X^2+X+2  1  1
 0  1  0  0  0  2 X^2+1 X+3  1 X^2+1  1 X+1 X^2+X X^2+X  1 X^2 X+3  0  1 X^2+3  1  1 X^2+X X^2+3 X^2 X^2+X  1  1  1 X^2+X+2 X+2  0 X+3 X^2+X+2 X^2+X+2 X^2+X X^2+X+1  1
 0  0  1  0  1 X^2+X+2 X^2  X X^2+X X^2+1 X^2+1 X^2+X+3 X+3  1  3  1 X^2+X  3 X+1 X+3  2 X+2  1  1 X^2 X^2+2 X^2+1 X^2  1 X^2+3 X+1 X+1 X^2+X X^2+2  3  1 X^2 X^2+X+1
 0  0  0  1  1 X+1 X^2+X+1  2  1  0  1  3 X+2 X^2+X+3 X+2 X+2 X^2+X+2 X+1 X^2+2 X^2+1 X^2+X X^2+X+3 X^2+1  X X^2+X X^2+X+1 X^2+X+3 X+3 X^2+X+3 X^2+X+2 X+1  X X+3  1  2 X^2+2 X^2+X+2 X^2+X
 0  0  0  0  2  0  0  0  0  2  2  2  2  2  2  2  0  2  2  0  2  2  0  0  2  2  0  2  0  0  0  0  2  0  0  2  2  2

generates a code of length 38 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+475x^32+1874x^33+5207x^34+8836x^35+15221x^36+21600x^37+24365x^38+21590x^39+16203x^40+8732x^41+4457x^42+1756x^43+571x^44+112x^45+51x^46+8x^47+9x^48+2x^49+2x^55

The gray image is a code over GF(2) with n=304, k=17 and d=128.
This code was found by Heurico 1.16 in 73.6 seconds.