The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+106x^32+918x^33+2520x^34+5018x^35+7485x^36+10880x^37+11715x^38+10842x^39+7761x^40+4962x^41+2179x^42+822x^43+203x^44+84x^45+17x^46+6x^47+12x^48+4x^49+1x^50

The gray image is a code over GF(2) with n=304, k=16 and d=128.
This code was found by Heurico 1.16 in 18.6 seconds.