The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+107x^60+208x^61+370x^62+518x^63+636x^64+680x^65+641x^66+718x^67+720x^68+714x^69+670x^70+572x^71+427x^72+392x^73+285x^74+186x^75+159x^76+60x^77+36x^78+34x^79+26x^80+8x^81+12x^82+4x^83+4x^84+2x^85+2x^86

The gray image is a code over GF(2) with n=272, k=13 and d=120.
This code was found by Heurico 1.16 in 3.76 seconds.