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

generates a code of length 69 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+139x^62+12x^63+181x^64+44x^65+216x^66+108x^67+279x^68+172x^69+264x^70+132x^71+189x^72+36x^73+89x^74+4x^75+87x^76+4x^77+48x^78+24x^80+11x^82+6x^84+1x^86+1x^112

The gray image is a code over GF(2) with n=276, k=11 and d=124.
This code was found by Heurico 1.16 in 32.4 seconds.