The generator matrix

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

generates a code of length 71 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+62x^62+254x^63+547x^64+700x^65+993x^66+1124x^67+1343x^68+1130x^69+1532x^70+1402x^71+1448x^72+1112x^73+1286x^74+1018x^75+744x^76+552x^77+484x^78+280x^79+192x^80+84x^81+53x^82+18x^83+13x^84+6x^85+6x^86

The gray image is a code over GF(2) with n=284, k=14 and d=124.
This code was found by Heurico 1.16 in 12.3 seconds.