The generator matrix

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

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+160x^70+120x^71+382x^72+248x^73+412x^74+296x^75+410x^76+208x^77+362x^78+296x^79+369x^80+248x^81+254x^82+120x^83+114x^84+30x^86+20x^88+16x^90+13x^92+12x^94+2x^98+2x^100+1x^108

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 2.31 seconds.