The generator matrix

 1  0  0  0  0  0  1  1  1  2  1  1  1  2  1  1  1  1  0  2  1  1  1  1  1  1  0  1  0  0  1  1  0  0
 0  1  0  0  0  0  0  0  0  0  2  1  3  1  2  3  2  3  2  1  0  0  3  3  1  1  0  1  2  1  1  2  0  1
 0  0  1  0  0  0  0  0  0  0  3  1  2  3  0  0  2  1  1  1  3  2  2  3  0  3  1  3  2  2  0  0  1  1
 0  0  0  1  0  0  2  1  3  1  1  2  3  3  1  1  1  3  0  1  0  2  0  1  0  0  3  3  1  2  1  0  2  0
 0  0  0  0  1  0  3  1  2  3  0  0  0  0  0  2  3  2  3  0  3  3  2  3  2  0  2  0  1  3  3  3  1  1
 0  0  0  0  0  1  1  2  3  3  0  0  0  0  2  3  1  0  2  1  3  0  2  2  3  1  3  3  0  1  3  3  0  2

generates a code of length 34 over Z4 who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+72x^26+150x^27+202x^28+248x^29+249x^30+254x^31+332x^32+356x^33+349x^34+372x^35+321x^36+328x^37+275x^38+216x^39+151x^40+84x^41+71x^42+30x^43+17x^44+8x^45+8x^46+2x^47

The gray image is a code over GF(2) with n=68, k=12 and d=26.
This code was found by Heurico 1.16 in 0.892 seconds.