The generator matrix

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

generates a code of length 69 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+122x^65+264x^66+258x^67+284x^68+276x^69+242x^70+244x^71+168x^72+114x^73+58x^74+10x^75+2x^76+2x^86+1x^88+2x^90

The gray image is a code over GF(2) with n=552, k=11 and d=260.
This code was found by Heurico 1.16 in 0.359 seconds.