The generator matrix

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

generates a code of length 77 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+108x^72+56x^73+152x^74+64x^75+142x^76+52x^77+130x^78+36x^79+143x^80+16x^81+64x^82+24x^83+10x^84+4x^85+2x^86+4x^87+8x^88+4x^90+2x^92+1x^100+1x^132

The gray image is a code over GF(2) with n=308, k=10 and d=144.
This code was found by Heurico 1.16 in 0.29 seconds.