The generator matrix

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

generates a code of length 68 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+74x^58+170x^59+311x^60+434x^61+493x^62+832x^63+1026x^64+1182x^65+1405x^66+1500x^67+1551x^68+1514x^69+1503x^70+1262x^71+995x^72+750x^73+465x^74+312x^75+236x^76+120x^77+80x^78+58x^79+30x^80+28x^81+12x^82+26x^83+8x^84+4x^85+2x^92

The gray image is a code over GF(2) with n=272, k=14 and d=116.
This code was found by Heurico 1.16 in 16.6 seconds.