The generator matrix

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

generates a code of length 38 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 33.

Homogenous weight enumerator: w(x)=1x^0+62x^33+122x^34+436x^35+298x^36+920x^37+475x^38+912x^39+253x^40+416x^41+101x^42+60x^43+21x^44+8x^45+5x^46+2x^48+2x^49+1x^50+1x^52

The gray image is a code over GF(2) with n=304, k=12 and d=132.
This code was found by Heurico 1.16 in 0.297 seconds.