The generator matrix

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

generates a code of length 68 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+120x^60+996x^61+2452x^62+4488x^63+7735x^64+9928x^65+14798x^66+15884x^67+18863x^68+15676x^69+14428x^70+10340x^71+7504x^72+4088x^73+2250x^74+852x^75+376x^76+184x^77+52x^78+20x^79+20x^80+8x^81+4x^82+5x^84

The gray image is a code over GF(2) with n=544, k=17 and d=240.
This code was found by Heurico 1.16 in 153 seconds.