The generator matrix

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

generates a code of length 70 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+220x^66+233x^68+238x^70+141x^72+108x^74+38x^76+30x^78+1x^80+8x^82+4x^90+1x^92+1x^96

The gray image is a code over GF(2) with n=280, k=10 and d=132.
This code was found by Heurico 1.16 in 28.5 seconds.