The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  1  2  1  1  1  1  0  1  0  X  1  X  0  1  1  X  1  1  2  1  1  2  2  1  X  X  1  1  X  X  1  X  X
 0  X  0  0  0  X X+2  X  0  2  2  0  X X+2  X X+2 X+2 X+2 X+2  2  0  0 X+2  2 X+2  0  2 X+2  X  2 X+2  X  0  2  2 X+2  2  2 X+2  2  0  X X+2  X  2  2 X+2  2 X+2  2 X+2  0  0  2  2  X  X  2 X+2  2  2 X+2 X+2  0 X+2  0  0 X+2
 0  0  X  0  X  X X+2  0  0  0 X+2 X+2  X  X  2  0  X  2  0 X+2 X+2  2 X+2  2  0  2  X  0  X  X  0  X  0  X  0 X+2  X  0  0  X  X  2 X+2 X+2  2  2  2  X  X  0  X X+2 X+2  0  X  0  0  X X+2  X  X  2  0  X  X  2  X  2
 0  0  0  X  X  0 X+2  X  2 X+2  X  2  2  X  X  2  0 X+2  0  X  2  X  X  0  0  X  2 X+2  X  X X+2  2  0  0  X X+2 X+2  0  0  0  0  0  2  X X+2 X+2  2  2 X+2  0 X+2 X+2 X+2  X  0  2  X  X X+2  0  0  2  2  2  0  X  2  2
 0  0  0  0  2  0  0  0  2  0  0  0  0  0  0  2  2  2  2  2  0  2  2  0  2  0  2  2  0  0  0  2  2  0  0  0  0  2  0  0  2  2  0  2  2  2  0  2  2  0  0  2  2  2  2  2  0  2  0  2  2  0  0  0  0  2  0  2
 0  0  0  0  0  2  0  2  0  0  2  2  0  2  2  0  0  0  2  2  2  0  0  2  0  2  2  2  0  0  0  2  0  0  2  2  0  2  2  0  0  2  2  0  2  0  0  2  2  0  0  2  2  2  2  2  2  0  0  0  2  2  0  0  0  2  0  0
 0  0  0  0  0  0  2  2  2  2  0  0  2  0  0  0  0  0  2  0  2  0  2  2  2  2  2  0  0  0  2  2  0  0  0  2  0  2  0  2  2  2  2  2  2  2  2  2  0  2  0  0  2  0  2  0  0  0  0  2  0  2  0  2  2  0  0  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+198x^60+24x^61+280x^62+68x^63+436x^64+176x^65+436x^66+260x^67+524x^68+224x^69+432x^70+172x^71+296x^72+80x^73+174x^74+12x^75+154x^76+8x^77+78x^78+43x^80+6x^82+11x^84+2x^86+1x^100

The gray image is a code over GF(2) with n=272, k=12 and d=120.
This code was found by Heurico 1.16 in 45.8 seconds.