The generator matrix

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

generates a code of length 42 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+18x^38+60x^39+77x^40+196x^41+365x^42+184x^43+49x^44+36x^45+28x^47+4x^49+1x^50+4x^53+1x^76

The gray image is a code over GF(2) with n=336, k=10 and d=152.
This code was found by Heurico 1.16 in 0.079 seconds.