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

generates a code of length 67 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+80x^62+206x^64+832x^66+784x^68+32x^70+16x^72+32x^74+16x^76+48x^78+1x^128

The gray image is a code over GF(2) with n=536, k=11 and d=248.
This code was found by Heurico 1.16 in 0.407 seconds.