The generator matrix

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

generates a code of length 79 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+111x^70+282x^72+24x^73+362x^74+132x^75+395x^76+252x^77+492x^78+248x^79+426x^80+208x^81+362x^82+116x^83+231x^84+28x^85+151x^86+16x^87+124x^88+72x^90+38x^92+18x^94+6x^96+1x^120

The gray image is a code over GF(2) with n=316, k=12 and d=140.
This code was found by Heurico 1.16 in 1.9 seconds.