The generator matrix

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

generates a code of length 70 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+203x^64+32x^65+220x^66+96x^67+250x^68+128x^69+200x^70+128x^71+258x^72+96x^73+220x^74+32x^75+162x^76+13x^80+4x^84+4x^88+1x^112

The gray image is a code over GF(2) with n=280, k=11 and d=128.
This code was found by Heurico 1.16 in 10.3 seconds.