The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X X X X X 1 1 2 0 X X 1 2 0 1 2 2X 2 2X X X X
0 2X+2 0 2X+2 2X 2 2X 2 0 2X+2 0 2X+2 2X 2 2X 2 2X+2 2X+2 2 0 2X 2 0 2X 2X+2 2 0 2X 0 2X+2 2 2X 2 2 2 2 2X+2 2X+2 2
0 0 2X 2X 2X 2X 0 0 0 0 2X 2X 2X 2X 0 0 0 2X 2X 2X 2X 0 0 0 0 2X 0 0 2X 2X 0 2X 2X 0 0 2X 0 2X 2X
generates a code of length 39 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 38.
Homogenous weight enumerator: w(x)=1x^0+12x^38+96x^39+13x^40+2x^42+2x^44+1x^46+1x^54
The gray image is a code over GF(2) with n=312, k=7 and d=152.
This code was found by Heurico 1.16 in 0.032 seconds.