The generator matrix

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

generates a code of length 77 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+82x^69+343x^70+416x^71+468x^72+646x^73+645x^74+656x^75+676x^76+658x^77+611x^78+652x^79+565x^80+460x^81+418x^82+278x^83+234x^84+178x^85+77x^86+34x^87+36x^88+22x^89+17x^90+10x^91+2x^92+2x^93+1x^94+2x^95+2x^96

The gray image is a code over GF(2) with n=308, k=13 and d=138.
This code was found by Heurico 1.16 in 4.45 seconds.