The generator matrix

 1  0  1  1  1 X+2  1  1  2  1  X  1  1  1 X+2  0  1 X+2  1  1  1  1  2  1  1  1  2  1  1  0  1  1 X+2  1  X  1  0  1  1  X  X  1  0  1  X  1  1 X+2  1  0  1  1  1 X+2  0  1  1  1  1 X+2  1  1 X+2  1  1  X  1  1
 0  1  1  0 X+3  1  X X+1  1  1  1  0 X+3 X+2  1  1  X  1 X+1  3 X+2  0  1  3  1 X+1  1 X+1 X+2  1  0  2  1 X+2  1  1  1  1  0  1  1  1  1 X+1  1  1  0  1 X+2  1 X+2 X+3 X+2  1  0  3 X+2 X+3 X+1  1  1  3  1 X+3  3  2 X+3 X+1
 0  0  X  0 X+2  0  0  0  2  2  2  X  0  X X+2 X+2  X  X X+2  X  0  X  X  0  X X+2  2  X  X  2  X  0  2  2 X+2  0  2  0  X X+2  2 X+2  X X+2 X+2  2 X+2 X+2 X+2 X+2 X+2  X  X  0  X  2  0  2 X+2  X  0  0  2 X+2  0  2  X  2
 0  0  0  X  0  0  X  2 X+2  X  X  X  X X+2 X+2 X+2  2  0 X+2  X  2  2  2  0  X  0  0 X+2  X  0  X  X  X  0  0 X+2 X+2  2 X+2 X+2 X+2  0  X  2  2  0  2 X+2  2  2  2  0  X  0  0 X+2 X+2  X  2  2  2  X  2  X  0 X+2  0  2
 0  0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  2  2  2  0  2  2  0  2  0  2  2  0  0  0  2  2  0  0  2  0  0  2  2  0  2  0  2  2  2  2  0  2  2  0  2  2  2  0  2
 0  0  0  0  0  2  0  2  2  2  2  2  2  2  0  0  2  0  0  0  0  2  0  2  0  0  2  0  2  2  0  2  0  2  2  0  0  0  0  2  0  2  2  2  2  0  2  2  0  2  0  0  0  0  0  2  0  0  2  2  0  2  0  0  0  2  2  2
 0  0  0  0  0  0  2  0  2  2  0  2  0  0  2  0  0  2  0  2  0  0  2  2  0  2  0  2  0  2  2  0  0  0  0  2  0  2  0  2  2  2  2  0  2  0  2  0  2  0  0  0  2  0  2  0  2  0  2  2  2  0  2  0  2  2  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+229x^60+60x^61+542x^62+216x^63+855x^64+288x^65+982x^66+432x^67+1102x^68+496x^69+956x^70+312x^71+753x^72+176x^73+392x^74+64x^75+189x^76+4x^77+50x^78+59x^80+18x^82+8x^84+4x^86+3x^88+1x^96

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 84.4 seconds.