The generator matrix

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

generates a code of length 68 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+274x^57+718x^58+1428x^59+2210x^60+3462x^61+4618x^62+6170x^63+7446x^64+9572x^65+10374x^66+12542x^67+12170x^68+12986x^69+11283x^70+10212x^71+7665x^72+6132x^73+4257x^74+3246x^75+1849x^76+1108x^77+647x^78+360x^79+196x^80+62x^81+39x^82+24x^83+15x^84+4x^85+2x^87

The gray image is a code over GF(2) with n=272, k=17 and d=114.
This code was found by Heurico 1.13 in 233 seconds.