The generator matrix

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

generates a code of length 69 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+302x^61+440x^62+804x^63+846x^64+1298x^65+1215x^66+1482x^67+1226x^68+1516x^69+1202x^70+1588x^71+918x^72+1140x^73+757x^74+700x^75+364x^76+250x^77+148x^78+96x^79+35x^80+34x^81+9x^82+2x^83+2x^84+4x^85+2x^86+3x^90

The gray image is a code over GF(2) with n=276, k=14 and d=122.
This code was found by Heurico 1.16 in 53.5 seconds.