The generator matrix

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

generates a code of length 69 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+116x^60+876x^61+2009x^62+5340x^63+8209x^64+14634x^65+20091x^66+28650x^67+31503x^68+38022x^69+32627x^70+30066x^71+19750x^72+14444x^73+7859x^74+4518x^75+1833x^76+1024x^77+337x^78+108x^79+58x^80+34x^81+16x^82+4x^83+2x^84+6x^85+5x^86+2x^87

The gray image is a code over GF(2) with n=552, k=18 and d=240.
This code was found by Heurico 1.16 in 607 seconds.