The generator matrix

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

generates a code of length 69 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+144x^65+161x^66+160x^67+70x^68+128x^69+61x^70+90x^71+22x^72+62x^73+31x^74+22x^75+14x^76+16x^77+17x^78+12x^79+5x^80+2x^81+2x^83+2x^86+2x^87

The gray image is a code over GF(2) with n=276, k=10 and d=130.
This code was found by Heurico 1.16 in 75.4 seconds.