The generator matrix

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

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+211x^60+100x^61+482x^62+304x^63+702x^64+532x^65+851x^66+552x^67+837x^68+668x^69+773x^70+544x^71+581x^72+284x^73+373x^74+72x^75+154x^76+16x^77+85x^78+31x^80+24x^82+9x^84+4x^86+1x^88+1x^92

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 9.57 seconds.