The generator matrix

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

generates a code of length 69 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+70x^61+202x^62+418x^63+510x^64+556x^65+683x^66+668x^67+738x^68+814x^69+713x^70+622x^71+579x^72+474x^73+353x^74+302x^75+198x^76+88x^77+90x^78+32x^79+12x^80+42x^81+3x^82+6x^83+8x^84+4x^85+3x^86+1x^88+1x^90+1x^96

The gray image is a code over GF(2) with n=276, k=13 and d=122.
This code was found by Heurico 1.16 in 3.49 seconds.