The generator matrix

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

generates a code of length 77 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+198x^71+277x^72+442x^73+403x^74+508x^75+350x^76+342x^77+263x^78+282x^79+181x^80+198x^81+151x^82+152x^83+84x^84+102x^85+43x^86+52x^87+17x^88+16x^89+18x^90+8x^91+2x^92+4x^93+2x^94

The gray image is a code over GF(2) with n=308, k=12 and d=142.
This code was found by Heurico 1.11 in 0.5 seconds.