The generator matrix

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

generates a code of length 68 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+71x^62+162x^63+192x^64+200x^65+190x^66+168x^67+186x^68+204x^69+147x^70+142x^71+135x^72+82x^73+64x^74+54x^75+19x^76+4x^77+2x^78+6x^80+2x^81+4x^82+2x^83+4x^84+4x^85+2x^86+1x^92

The gray image is a code over GF(2) with n=272, k=11 and d=124.
This code was found by Heurico 1.16 in 0.4 seconds.