The generator matrix

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

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+52x^61+218x^62+396x^63+530x^64+488x^65+843x^66+664x^67+812x^68+560x^69+832x^70+584x^71+588x^72+390x^73+440x^74+232x^75+213x^76+156x^77+98x^78+38x^79+22x^80+14x^81+1x^82+4x^83+7x^84+4x^85+2x^87+3x^88

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 3.51 seconds.