The generator matrix

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

generates a code of length 77 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+54x^70+214x^71+306x^72+344x^73+416x^74+418x^75+366x^76+316x^77+303x^78+264x^79+255x^80+222x^81+147x^82+146x^83+78x^84+64x^85+73x^86+36x^87+30x^88+14x^89+13x^90+6x^91+4x^92+2x^94+2x^95+2x^99

The gray image is a code over GF(2) with n=308, k=12 and d=140.
This code was found by Heurico 1.16 in 1.12 seconds.